Control system for mobile NOx SCR applications

ABSTRACT

A diesel powered vehicle is provided with an SCR system which uses an external reducing reagent to convert NOx emissions in a manner which accounts for the effects of NOx transient emissions on the reducing catalyst. Actual NOx emissions produced by the engine are filtered using a variable NOx time constant in turn correlated to the reductant/NOx storage capacity of the reducing catalyst at its current temperature to account for changes in the SCR system attributed to NOx transient emissions. Catalyst temperature is filtered using a variable catalyst time, constant corresponding to current space velocity of the exhaust gas to account for changes in the catalyst temperature attributed to NOx transient emissions. The reductant is metered on the basis of the filtered, corrected NOx concentration applied at a NSR ratio based, in turn, on the filtered, corrected reducing catalyst temperature.

[0001] This invention relates generally to nitrogen oxide (NOx)emissions produced by internal combustion engines in a vehicle and moreparticularly to a system for controlling reduction of the NOx emissionsby means of a selective catalytic reduction (SCR) method.

[0002] The invention is particularly applicable to and will be describedwith specific reference to a control system for regulating the supply ofan external reductant, ammonia, to a reducing catalyst in an SCR systemtaking into account the effect of NOx transient emissions produced invehicles powered by diesel engines. However, those skilled in the artwill recognize that the control system has broader applications and maybe applied to SCR systems using other reductants such as fuel oil orhydrocarbons as well as SCR systems used in other mobile internalcombustion engine applications, such as gasoline engines employing “leanburn” techniques.

INCORPORATION BY REFERENCE

[0003] The following patents and publications are incorporrated byreference herein and made a part hereof:

[0004] 1) U.S. Pat. No. 4,403,473, to John R. Gladden; dated Sep. 13,1983, entitled: “AMMONIA/FUEL RATIO CONTROL SYSTEM FOR REDUCING NITROGENOXIDE EMISSIONS”;

[0005] 2) SAE Paper No. 952493, by H. Luders, R. Backes, and G.Huthwohl, FEV Motoremtechnik and D. A. Ketcher, R. W. Horrocks, R. G.Hurley and R. H. Hammerle, Ford Motor Co., dated Oct. 16-19, 1995,entitled: “AN UREA LEAN NOx CATALYST SYSTEM FOR LIGHT DUTY DIESELVEHICLES” (See page 7);

[0006] 3) SAE Paper No. 921673, by J. Walker, Ortech and B. K.Speronello, Engelhard Corp., dated Sep. 14-17, 1992, entitled:“DEVELOPMENT OF AN AMMONIA/SCR NOx REDUCTION SYSTEM FOR A HEAVY DUTYNATURAL GAS ENGINE”;

[0007] 4) U.S. Pat. No. 5,606,855, to Naoki Tomisawa, dated Mar. 4,1997, entitled: “APPARATUS AND METHOD FOR ESTIMATING THE TEMPERATURE OFAN AUTOMOTIVE CATALYTIC CONVERTER”; and,

[0008] 5) U.S. Pat. No. 5,490,064, to Minowa et al., dated Feb. 6, 1996,entitled: “CONTROL UNIT FOR VEHICLE AND TOTAL CONTROL SYSTEM THEREFOR”.

[0009] None of the material cited above form any part of the presentinvention. The material is incorporated by reference herein so thatdetails relating to SCR systems such as the operation of the SCR systemswith ammonia or hydrocarbon reductants, the metering, of the reductants,principles and control of engine operation etc., need not be set forthor described in detail herein.

BACKGROUND

[0010] This invention is directed to the removal of nitrogen oxides(NOx) from the exhaust gases of internal combustiobn engine,particularly diesel engines, which operate at combustion conditions withair in large excess of that required for stoichiometric combustion,i.e., lean. Unfortunately, the presence of excess air makes thecatalytic reduction of nitrogen oxides difficult. Emission regulationsimpose a limit on the quantity of specific emissions, including NOx,that a vehicle can emit during a specified drive cycle, such as i) forlight duty trucks, an FTP (“federal test procedure”) in the UnitedStates or an MVEG (“mobie vehicle emissions group”) in Eulrope or ii)for heavy duty trucks, a Heavy Duty Cycle in the United States or an ESC(European Steady State Cycle) or ETC (European Transient Cycle) inEurope. The regulations are increasingly limiting the amount of nitrogenoxides that can be emitted during the regulated drive cycle.

[0011] There are numerous ways known in the art to remove NOx from awaste gas. This invention is directed to a catalytic reduction methodfor removing NOx. A catalytic reduction method essentially comprisespassing the exhaust gas over a catalyst bed in the presence of areducing gas to convert the NOx into nitrogen. Conventionally, there arethree ways to treat vehicular exhaust to reduce NOx. The first method isnon-selective catalyst reduction (NSCR). The second way is selectivenon-catalytic reduction (SNCR) and the last method is selective catalystreduction (SCR). This invention relates to SCR systems.

[0012] In diesel engines, sufficient NOx reduction to meet currentregulations has been achieved by combustion modifications in the dieselengine by, for example, incorporating EGR. Projected emission levels aresuch that combustion and engine modifications will not be sufficient tomeet the more stringent levels. Because of excess oxygen present indiesel exhaust gases, the opportunity for NOx reduction under rich orstoichiometric air/fuel is not possible. SCR is a technology that hasbeen shown effective in removing NOx from oxygen rich exhaust. A numberof SCR systems have been developed which, because of infrastructureconcerns, have used diesel fuel or diesel oil as the reductant source.Unfortunately, as of this date, an HC reducing catalyst has not yet beendeveloped which has sufficient activity and is effective over the entireoperating range of the diesel engine.

[0013] A common nitrogen oxide reducing agent, long used in industrialprocesses, is ammonia. NOx reducing catalysts have been developed whichare effective over the operating range of the engine. Despite theinfrastructure concerns relating to the use of urea in a mobileapplication as well as the potentially dangerous risks of ammoniabreak-through or slip, ammonia SCR systems are becoming the favoredchoice for mobile applications to meet the more stringent NOx emissions.This is, among other reasons, because of the high NOx conversionpercentages possible with ammonia coupled with the ability to optimizethe combustion process for maximum power output with minimum fuelconsumption.

[0014] Notwithstanding what may be said to be inherent advantages of anammonia based SCR system, the control systems to date have beenexcessively complicated and/or ineffective to control the SCR systemwhen the impact of NOx transient emissions on the SCR system isconsidered. As will be shown below, if the transient NOx emissions cannot be adequately reduced by the SCR control system, then stringent NOxemission regulations will not be met.

[0015] Early patents controlled ammonia metering by considering theemissions to be controlled at steady state conditions. For example, U.S.Pat. No. 4,403,473 to Gladden (Sep. 13, 1983) considered NOx emissionsat various speed ranges and concluded that a linear relationship existsbetween fuel flow and NOx. (Earlier Gladden U.S. Pat. No. 4,188,364,Feb. 12, 1980 concluded that ammonia catalyst adsorbed ammonia attemperatures lower than 200° C. and desorbed at temperatures between200-800° C., the SCR system should operate at higher, temperatures toachieve complete reaction between ammonia and NOx.) Thus, in Gladden'473, the fuel mass flow is sensed and NH₃ throttled at a percentage offuel flow provided the temperature of the gases in the catalyticconverter are within a set range. This basic control concept is usedtoday in most mobile, ammonia, SCR systems. For example, U.S. Pat. No.5,116,579 to Kobayashi et al. (May 26, 1992) additionally measures thehumidity of intake air and one or more operating parameters of enginepower, intake air temperature, fuel consumption and exhaust gastemperature to set an ammonia ratio control valve. The molar ratio ofammonia to NOx is set at less than one (sub-stoichiometric) to minimizeammonia slip.

[0016] Typically the reductant is pulse metered into the exhaust gasstream in a manner similar to that used for operating conventional fuelinjectors. In U.S. Pat. No. 4,963,332 to Brand et al. (Oct. 16, 1990),NOx upstream and downstream of the catalytic converter is sensed and apulsed dosing valve controlled by the upstream and downstream signals.In U.S. Pat. No. 5,522,218 to Lane et al. (Jun. 4, 1996), the pulsewidth of the reductant injector is controlled from maps of exhaust gastemperature and engine operating conditions such as engine rpm,transmission gear and engine speed.

[0017] As noted, the industrial art has long used ammonia in SCR systemsto control NOx emissions typically by set point control loops such asshown in U.S. Pat. No. 5,047,220 to Polcer (Sep. 10, 1991) in which adownstream NOx sensor is used to generate a trim signal in the controlloop. The industrial art has also recognized that changes in load fromthe turbine, furnace etc. affects the ammonia SCR systems. Thus in U.S.Pat. No. 4,314,345 to Shiraishi et al. (Feb. 2, 1982), variations inload are determined by sensing the temperature of the exhaust gas. Whenthe exhaust gases are at certain temperature ranges a variation in theload is assumed to occur and different or predicted NH3/NOx molar ratiosare used to account for the adsorption/desorption characteristics of thecatalyst. A more sophisticated molar ratio control system is disclosedin U.S. Pat. No. 4,751,054 to Watanabe. Watanabe uses not only upstreamand downstream NOx sensors but also temperature, flow rate and NH3detectors to set a mole ratio correcting signal. In U.S. Pat. No.4,473,536 to Carberg et al. (Sep. 25, 1984) a turbine's inlet airflow,discharge pressure, discharge temperature and mass fuel flow are sensedto predict NOx generated by the turbine which signal is corrected forNOx error by time delayed NOx sensor measurements. Carberg recognizesthat turbine load changes may change NOx emissions in a time framequicker than the 1 plus minute needed to determine the NOx emissions ina gas sample with conventional NOx sensors and thus makes a prediction,which can not be corrected in real time. The industrial systems, for themost part, do not operate under the highly transient conditions whichcharacterize vehicle engines producing sudden NOx transients. Industrialsystems also operate in an environment in which samples of the gas beingproduced can be taken to accurately determine the NOx content to trimthe ammonia metering valve in closed loop control.

[0018] In addition to systems which sense engine operating parameters tocontrol metering of ammonia or a reductant, there are other approachesused to control NOx emissions in mobile applications. In U.S. Pat. No.5,845,487 to Fraenkle et al. (Dec. 8, 1998), the exhaust gas temperatureis sensed. If the exhaust gas is outside the temperature limits at whichthe SCR system is effective i.e., below the operating temperature, thefuel injection timing to the engine is retarded, reducing the NOx viacombustion modifications. In U.S. Pat. No. 5,842,341 to Kibe (Dec. 1,1998) space velocity and exhaust gas temperature is measured todetermine the reductant quantity. In addition inlet and outlet catalyticconverter temperature is measured and reductant flow is decreased fromthe steady state conditions when the temperature differential betweeninlet and outlet begins to increase. The reductant, disclosed as HC inKibe's preferred embodiment, does not according to Kibe otherwisecontribute, by exothermic HC oxidation reactions, to heating of thecatalyst mass or bed. The reductant is decreased to keep the catalystwithin the operating temperature window.

[0019] Perhaps one of the more sophisticated approaches to usingurea/ammonia system in a mobile application is disclosed in a series ofpatents which include U.S. Pat. No. 5,833,932 to Schmelz (Nov. 10,1998); U.S. Pat. No. 5,785,937 to Neufert et al. (Jul. 28, 1998); U.S.Pat. No. 5,643,536 to Schmelz (Jul. 1, 1997); and U.S. Pat. No.5,628,186 to Schmelz (May 13, 1997). While these patents discussreducing reagents in a general sense, they are clearly limited tourea/ammonia reductants. According to this system, a catalytic converterhaving composition defined in the '932 patent, has a reducing agentstorage capacity per unit length that increases in the direction of gasflow. This allows for positioning of instrumentation along the length ofthe catalyst as disclosed in the '536 patent to determine the quantityof ammonia stored in the catalyst. The catalyst is charged with thereducing agent such that transient emissions can be converted by thereducing agent stored in the catalytic converter. The '186 patent,however, is directed as is the present invention, to a control systemnot limited to any specific catalyst. The '186 patent recognizes, asdoes several prior art references discussed in this section, that i)sudden increases in load require a decrease in the reducing agent (andsimilarly sudden decreases in load require an increase in the reducingagent) and ii) the temperature (the '186 patent also requires exhaustgas pressure) of the reducing catalyst affects its ability to store andrelease the reducing agent. The '186 patent measures, from changes ingas pressure and catalyst temperature, the rate at which the reducingagent is being adsorbed or desorbed from the catalyst. It thencalculates NOx emissions produced from the engine and sets asub-stoichiometric ratio of reducing agent/NOx emissions at which thereducing agent is metered to the catalyst. The metering reducing agentrate is then adjusted upward or downward to equal the measured rate ofreducing agent adsorption/desorption. A burner is provided to “empty”the catalyst apparently to assure a sound reference value upon enginestart for measurements and to guard against slip. Assuming theadsorption/desorption theory and measurement capability is “sound”, thesystem is sound although a large number of sensors and intensivecalculations appear to be required.

[0020] Within the literature, a significant number of articles have beenpublished investigating ammonia SCR NOx reducing systems and severalarticles have discussed control strategies to optimize the SCR NOxsystems investigated. In SAE paper 921673, entitled “Development of anAmmonia/SCR NOx Reduction System for a Heavy Duty Natural Gas Engine” byJ. Walker and B. K. Speronello, (September 1992), various quantities ofammonia were injected at various engine speeds and loads to obtainoptimum NOx, conversions at steady state engine speeds and loads. Thespeeds and loads were mapped and stored in a look-up table (specific foreach engine and each SCR catalyst) which was then accessed periodicallyto set an ammonia metering rate. This open loop, feed forward techniqueis conventionally used and produces good conversion ratios for steadystate conditions.

[0021] SAE paper 970185, “Transient Performance of a Urea deNOx Catalystfor Low Emissions Heavy-Duty Diesel Engines” by Dr. Cornelis Havenithand Ruud P. Verbeek (a co-inventor of the subject application) datedFebruary, 1997 investigates ammonia metering adjustments made duringtransient emissions. A pulsed urea dosage device is disclosed which usesspeed and load engine sensor data read into a control unit to pulse aquantity of ammonia in stoichiometric relationship to NOx emissions, atsteady state conditions. During step-urea, step-load and transientcycles, the stoichiometric relationship was decreased and a dynamiccontrol strategy of injecting additional quantifies of urea after thetransient or step or load was completed was adopted. A reduction in NOxemissions is reported although it is questionable whether the reductionwas achieved because of the dynamic control strategy the additionalreductant added during, the transient or a combination thereof.

[0022] SAE paper 925022, “Catalytic Reduction of NOx in Diesel Exhaust”by S. Lepperhoff, S. Huthwohl and F. Pischinger, March, 1992 is an earlyarticle that looked at step load changes to evaluate transient systems.The article recognizes that when the load on the engine changed atconstant rpm, the NOx emissions increase, the temperature increases andthe total exhaust flow increases. Response of the catalyst to stepchanges in the engine operating conditions are referred to as step loadtests. Ammonia slip occurred when engine load increased and the articleconcludes the slip is correlated to the ammonia stored in the catalyst.It was suggested that a control program or control system would have toconsider the, NOx emissions of the engine, the catalyst temperature andthe ammonia stored within the catalyst, to avoid ammonia slip.

[0023] SAE paper 952493, “An Urea Lean NOx Catalyst System for LightDuty Diesel Vehicles” by H. Luders, R. Backes, G. Huthwohl, D. A.Ketcher, R. W. Horrocks, R. G. Hurley, and R. H. Hammerle, October, 1995concludes that an ammonia SCR system can control NOx diesel emissions.The control strategy used in the study was similar to that disclosed inthe Gladden and Lane patents above i.e., a microprocessor mapped engineout NOx emissions and catalytic converter temperature. Engine out NOxwas derived from engine speed and torque. Space velocity (intake airmass flow) and catalyst temperature were then used with NOx out data toset a maximum NOx reduction rate. Transient operation was numericallymodeled from steady state conditions. Ammonia storage and thermalinertia was noted as factors affecting the conversion but the controlsystem discussed had no special provisions, other than numericalmodeling.

[0024] SAE paper 930363, “Off-Highway Exhaust Gas After-Treatment:Combining Urea-SCR, Oxidation Catalysis and Traps” by H. T. Hug, A.Mayer and A. Hartenstein, March, 1993, describes stoichiometricinjection of ammonia, without lag, based on engine mapped conditions.Catalyst porosity is stated to be important with respect to transientemissions. An injection nozzle for metering is disclosed.

[0025] An article entitled “NOx-Reduction in Diesel Exhaust Gas withUrea and Selective Catalytic Reduction” by M. Koebel, M. Elsener and T.Marti, published in Combustion Science and Technology, Vol 121, pp.85-102, 1996 describe experiments conducted “at abrupt load changes”. Anabrupt reduction in load did not cause ammonia slip but an abruptincrease in load did cause ammonia slip. The article observes that thecatalyst is saturated with adsorbed ammonia at lower temperatures; thatincreased load significantly increases NOx emissions; that increasedload increases, slowly, the temperature of the catalyst. Ammonia slipoccurring at the onset of the abrupt load change because of excessiveammonia present when the desorption of the ammonia is increased whilethe bulk at of the catalyst bed is too cool to effectively react thedesorbed ammonia with the higher level of NOx. This observation has beennoted in several of the prior art references discussed above. Therecommendation is to retard the addition of ammonia in relation to theload increase.

[0026] In general collective summary of the prior art referencesdiscussed above, it is known that ammonia SCR systems can be usedeffectively to control the emissions produced by vehicles powered bydiesel engines; that the reducing catalysts adsorbs and stores ammoniaat low temperatures and desorbs the stored ammonia at higher exhaust gastemperatures; that steady state NOx emissions, determined from mappedspeed and load engine conditions, can be readily controlled by meteringammonia in stoichiometric relationship to the NOx emissions; that it ispossible to pump urea, react urea to produce ammonia and preciselycontrol the rate of ammonia rejection to the exhaust gases bycontrolling pulsed injections of ammonia; and that transient emissionscause transient increases in NOx concentrations with attendant exhaustgas temperature increases requiring a reduction in the ammonia meteringrate to balance the increased ammonia present attributed to desorptionresulting from the temperature increase. Noticeably absent, from any ofthe mobile applications discussed, is a simple control system capable ofquickly and effectively adjusting the metering rate during transientemissions as well metering the reductant during steady state operatingconditions.

[0027] In this regard and as noted above, industrial processes, which donot have the sudden transient emission changes of a vehicularapplication, can utilize NOx sensors in a closed loop controlled throughset-point controllers. There are no commercially available NOx sensorswhich have the response time needed for vehicular applications. Thus anySCR control system for mobile applications will necessarily be openloop.

SUMMARY OF THE INVENTION

[0028] Accordingly, it is a principal object of the present invention toprovide a control for an NOx SCR mobile emission reduction system whichis able to control the system to reduce transient as well as steadystate NOx emissions without reductant slip.

[0029] This object along with other features of the invention isachieved in a method for reducing NOx emissions produced in mobilediesel applications by an external reductant supplied to an SCR systemcomprising the steps of a) sensing one or more engine operatingparameters to predict a concentration of NOx emissions indicative of theactual quantity of NOx emissions produced by the engine; b) when theactual concentration of NOx emissions changes and the temperature ofsaid reducing catalyst is within a set range, varying the actualconcentration of NOx emissions by a time constant to produce acalculated concentration of NOx emissions different than the actualconcentration of NOx emissions; and, c) metering the external reductantto the reducing catalyst in said SCR system at a rate sufficient tocause the reducing catalyst to reduce said calculated concentration ofNOx emissions whereby metering of the reductant accounts for the effectson said SCR system attributed to transient NOx emissions. Moreparticularly, the NOx constant acts to decrease the actual concentrationof NOx emissions when the NOx emissions increase to avoid: reductantslip and increase the actual NOx emissions when the NOx emissionsdecrease to utilize the catalyst reductant storage abilities.

[0030] In accordance with an important feature of the invention, the NOxtime constant is a function of the catalyst temperature within a settemperature range as that catalyst temperature relates to the capacityof any given catalyst to store reductant at that temperature. Generally,the storage ability of the catalyst decreases as the catalysttemperature increases within the catalyst temperature range whereby thereductant is metered, during and following an NOx transient, on thebasis of the ability of any specific catalyst used in the SCR system tostore the reductant thus minimizing the likelihood of reductant slip.

[0031] It is a distinct feature of the invention that the ability of anygiven catalyst to store reductant is expressed as the relative time ittakes for any given catalyst to store reductant at any given catalysttemperature to generate a varying time constant that can be accessedthrough a conventional look up table storing time constant-catalysttemperature relationships. The time constant is utilized to account forthe lag in the catalyst response to the NOx transient by modifying theNOx emission concentration in any number of ways, such as by determininga moving average of NOx emissions over varying time periods, each timeperiod correlated to a time constant in the look-up table for a thencurrent catalyst temperature, so that reductant dosage is determinedwithout having to sense numerous parameters and perform numerouscalculations to periodically determine current storage capacity of thecatalyst for setting the reductant metering rate.

[0032] However, it is a distinct feature of the invention to provide afilter to account for the lag in the catalyst system attributed totransient NOx emission by filtering the actual NOx emissions (increasingor decreasing) to NOx concentrations which do not exceed the catalyst'sability to store reductant at its current temperature in a responsiveand robust control. In accordance with this feature of the invention,the filter uses the capacity of the catalyst to store reductant at thelower temperatures of the catalyst temperature range while alsoproviding, when the reductant is aqueous urea, improved urea hydrolysisby the provision of two first order filters in series represented in thecontinuous time domain by the transfer function:${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

[0033] and

τ1=τ2=f(Cat)

[0034] When filtering the actual NOx emission concentration, thevariable NOx time constant, τNOx, is determined from the look-up tablenoted above as a function of the catalyst temperature. In accordancewith the broader scope of the invention, the second order filter iseffective to introduce a lag for any temperature dependent relationshipof the catalyst, including but not limited to those that are onlystraight line or constant approximations of the catalyst's ability tostore reductant at certain temperatures within a temperature range ofthe catalyst.

[0035] In accordance with another distinct aspect of the invention, thesystem employs a second order filter, as represented in the continuousform designated above, to account for the changing heat fronts movingthrough the catalyst bed which are attributed to NOx transient emissionsand produces a functional catalyst temperature which is a more accuratetemperature than that achieved by sensing pre or post or mid-bedcatalyst temperatures. In accordance with this aspect of the invention,(which is not limited in application to control systems which factor NOxconcentrations but can be applied to any mobile system which measures orsenses catalyst temperature for any reason), the catalyst time-constantτCat is a function of the space velocity of the exhaust gases throughthe catalyst.

[0036] In accordance with this distinct feature of the invention, amethod for determining the functional temperature of a catalyst in anexhaust system of a vehicle includes the steps of i) determining, bysensing or calculating, the temperature of the exhaust gases and thespace velocity of the exhaust gases through the catalyst and ii)filtering the exhaust gas temperature by a catalyst filter, to generatethe functional temperature of the catalyst. Significantly, the catalystfilter implements a time constant determined as a function of changingspace velocity to filter the exhaust gas temperature and is implementedin the continuous time domain by a second order filter as set forthabove.

[0037] In accordance with a still further feature of the invention, thetransfer function, H(s), for the NOx and catalyst filters of the presentinvention can be easily implemented in any number of discrete forms intothe vehicle's existing microprocessor because any of the conventionaldifference equations implementing the transfer function in discrete formare not memory intensive.

[0038] In accordance with yet another aspect of the invention, the twofirst order filters forming the functional catalyst temperature aresplit, upon engine shut-down, from a series relationship into twoindividual parallel operating first order filters with ambienttemperature fed as filter input to the temperature of the catalyst sothat after short engine stop/start periods, the cooled down temperatureof the catalyst is used in the second catalyst filter to preventreductant slip after engine restart. In accordance with this aspect ofthe invention, the cool down time constant, τCool, is determined as afunction of time elapsed from vehicle shut down or parameters thatrepresent difference in temperature. By arranging both filters inparallel so that each receives the same information, the second parallelfilter is prevented from freezing or drifting when the filters areswitched back to series relationship upon restart of the vehicle.

[0039] In accordance with a specific feature of the invention, theexternal reductant is ammonia and the storage capacity of the reducingcatalyst which is used to set the time constant NOx for any givencatalyst is a function of a) the surface area of the catalyst over whichthe exhaust gases flow, b) the number and strength ofadsorption/absorption sites on the surface area and c) the ability ofthe catalyst washcoat to store NOx at any given temperature within theset temperature range whereby a control method not only uses a wellknown reductant to optimize the performance of any given catalyst, butalso provides a method to optimally size a reducing catalyst for anygiven engine/vehicle combination to, meet regulated drive cycle NOxemission requirements.

[0040] In accordance with a still further feature of the invention, theexternal reductant is metered at a normalized stoichiometric ratio ofreductant to NOx emission established for the current functionalcatalyst temperature (as determined by the catalyst NOx constant)whereby each essential step of the method, i.e., the NOx emissions, thecatalyst functional temperature and the NSR ratio, have all beenadjusted to account for the inevitable effects on the SCR systemresulting from engine operating conditions producing NOx transientemissions which otherwise adversely affects the operation of the SCRsystem. Again, the current state of the catalyst does not have to besensed nor intensive calculations run based on sensed catalyst state toset the reductant rate.

[0041] Still another specific and inclusive feature of the invention isto provide a method for metering an external reductant to a reducingcatalyst in an SCR system applied to a vehicle powered by an internalcombustion engine which includes the steps of

[0042] a) sensing operating conditions of the vehicle and engine togenerate, by calculation and/or measurement, signals indicative of theactual quantity of NOx emissions emitted by the engine, the temperatureof the exhaust gas and the space velocity of the exhaust gas;

[0043] b) filtering, when the temperature of the catalyst is within aset temperature range, the actual NOx emission signal by an NOx timeconstant to produce a calculated NOx signal different than the actualNOx signal when the NOx signal is changing;

[0044] c) filtering the exhaust gas temperature signal by a catalysttime constant to produce a functional catalyst temperature signaldifferent than the exhaust gas temperature when the space velocitysignal changes;

[0045] d) factoring the functional catalyst temperature signal and thespace velocity signal to generate a NSR signal indicative of anormalized stoichiometric ratio of reductant to NOx emissions; and,

[0046] e) metering the reductant to the reducing catalyst by factoringthe calculated NOx signal by the NSR signal to produce a metering signalcontrolling a metering device for the external reductant.

[0047] It is a general object of the invention to provide a nitrogenbased SCR control system for NOx emissions produced by diesel poweredvehicles.

[0048] It is another general object of the invention to provide anexternal reductant SCR control system for mobile IC engine applicationswhich minimizes reductant slip while utilizing the ability of the SCRcatalyst to store reductant.

[0049] It is an object of the invention to provide a control system formobile NOx SCR systems having any one or any combination of thefollowing characterizing features:

[0050] a) Ability to control reduction of transient as well as steadystate NOx emissions;

[0051] b) Ability to prevent reductant slip during NOx transientemissions;

[0052] c) Simple to implement in programmable routines not subject toextensive memory requirements stored in the ECU;

[0053] d) Robust, stable and not subject to significant drift over time;

[0054] e) Able to account for thermal aging of catalyst;

[0055] f) Easily implemented in OBD diagnostic systems;

[0056] g) Inexpensive because it requires no additional parts orcomponents other than what is currently used in state-of-art systems;

[0057] h) Not limited to any specific driving cycle or test cycle; and

[0058] i) Insensitive to arbitrary changes to temperature and/or loadand/or NOx emissions.

[0059] Another distinct but related object of the invention to provide amethod for determining the functional catalyst temperature of SCRcatalysts for use in any control type system resulting from changesattributed to NOx transient emissions notwithstanding what methodologyis used to establish the catalyst temperature at steady stateconditions.

[0060] Still another stand alone but related object of the invention isto provide a method for ascertaining the start-up temperature of anycatalyst in any emission system.

[0061] Still yet another object of the invention is to provide a controlsystem for a mobile IC engine SCR application which is able to accountfor changes to the SCR system attributed to NOx transient emissionsnotwithstanding the fact that such control systems may employ NOx and/orreductant sensors assuming commercially acceptable, time responsivesensors are developed for mobile engine applications.

[0062] Still another object of the invention is to provide an SCRcontrol system for mobile IC applications using an external reductantwhich can function with any design or type of reducing catalyst used inthe SCR system.

[0063] Another object of the invention is the provision of an SCRcontrol system for mobile IC applications using an external reductantwhich provides a basis for optimizing the selection of any specificreducing catalyst for any given engine/vehicle combination.

[0064] Yet another object of the invention is to provide an SCR controlsystem for an external reductant which determines and uses thestorage/release capacity of reductant and NOx emissions for any givenSCR catalyst to control reductant metering in a manner that accounts forthe capability of that specific catalyst to reduce NOx emissions as aresult of NOx transient emissions produced by the engine.

[0065] A still further object of the invention is the provision of acontrol system for an external reductant applied to a mobile IC enginehaving an SCR system in which reductant usage is minimized whilemaintaining high NOx conversion.

[0066] Another object of the invention is to provide a control systemfor an external reductant SCR system which emulates the lag of thecatalyst following NOx transient emissions by use two simple first orderfilters in series having time constants determined as a function oftemperature.

[0067] These and other objects, features and advantages of the presentinvention will become apparent to those skilled in the art upon readingand understanding the Detailed Description of the Invention set forthbelow taken in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The invention may take form in certain parts and an arrangementof parts taken together and in conjunction with the attached drawingswhich form a part of the invention and wherein:

[0069]FIG. 1 is a graph of NOx emissions produced in the exhaust gasesof a diesel powered vehicle during the European MVEG cycle;

[0070]FIG. 2A depicts a series of graphs showing torque, inlet andoutlet catalyst temperatures and NOx emissions produced over time duringa step load test of a diesel powered vehicle;

[0071]FIG. 2B depicts a series of graphs similar to FIG. 2A for arapidly sequencing step load test;

[0072]FIG. 3 is a schematic representation of an SCR system controlledby the method of the invention;

[0073]FIG. 4 is a flow chart indicative of the steps used in the presentinvention to control the SCR system;

[0074]FIG. 5 is a map of space velocity and catalyst temperaturevariables resulting in various normalized stoichiometric ratios;

[0075]FIG. 6 is a schematic representation of the NOx filter of thepresent invention in a discrete form;

[0076]FIGS. 7A and 7B are schematic representations of first orderfilters suitable for use in the present invention;

[0077]FIG. 7C is a graph depicting the filter effects of the filtersshown in FIGS. 7A and 7B;

[0078]FIG. 8 is a graph depicting the filter effect of the invention ona step load transient emission;

[0079]FIG. 9 is a graph of an ETC test plotting the functional catalysttemperature predicted by the invention, the sensed mid-bed catalysttemperature and the sensed average catalyst temperature;

[0080]FIG. 10 is a schematic representation of the TCat filter of thepresent invention in a discrete form;

[0081]FIG. 11 is a constructed graph indicative of the variable NOxconstant used in the present invention, i.e., τNOx; and,

[0082]FIG. 12 is a graph of a portion of an ETC cycle showing ammoniaslip for systems which metered the reductant based on actual NOxemissions compared to a system using the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0083] Referring now to the drawings wherein the showings are for thepurpose of illustrating a preferred embodiment of the invention only andnot for the purpose of limiting the same, there is shown in FIG. 1 anMVEG test conducted with a test vehicle equipped with a 1.9 literturbocharged, direct injection (TDI) diesel engine, i.e., a light dutytest vehicle. The invention will be described throughout as applicableto a diesel engine, but as indicated above, the invention, in itsbroader sense, is applicable to any internal combustion (IC) engine,such as gasoline fuel type engines operated lean or with “lean burn”engine fuel strategy.

[0084] In FIG. 1, the European MVEG cycle is plotted in seconds on thex-axis with the nitrogen oxides (NOx) emitted by the vehicle during thedrive cycle plotted on the left-hand y-axis and the vehicle speedplotted in km/hr on the right-hand y-axis. The lower trace identified bythe reference numeral 10 is a plot of the vehicle speed over the timedportion of the drive cycle. The uppermost plot identified by referencenumeral 12 are the NOx emissions produced by the diesel powered vehicleduring a regulated drive cycle and is characterized, ratherdramatically, by “spikes” of NOx transient emissions. Several factualobservations concerning the graph of FIG. 1 should be noted as follows:

[0085] 1) When the vehicle is traveling at a constant speed, the NOxemissions are somewhat constant. This can be shown, for example, bylooking at that portion of the vehicle speed plot designated byreference numeral 10A and comparing it to the generally flat portion ofNOx emissions generated during that time period in the NOx plot sectiondesignated by reference numeral 12A. Assuming load is constant, constantvehicle speed will produce constant or “steady state” NOx emissions. Asdiscussed in the Background, NOx control strategies in use today arebased on steady state conditions. Thus when an SCR system uses anexternal reductant, the external reductant is metered, under today'sstrategies, at a rate sufficient to reduce the NOx constant emissionsproduced at 12A. If the speed (and load) of the vehicle remain fairlyconstant, as in most industrial processes, high NOx conversionefficiencies can be obtained. FIG. 1 shows why that control philosophycan not work with a mobile IC engine application.

[0086] 2) When the vehicle accelerates, such as indicated by theacceleration designated as reference numeral 10B, the NOx emissionscorrespondingly and dramatically increase or “spike” as shown by spike12B and the spike or pulse or increase in NOx emissions is commonlyreferred to as an NOx transient. Further the faster the acceleration (orrate at which load is applied to the vehicle), the greater the NOxtransient emission. The time scale used in FIG. 1 does not permitscrutiny of each of the transient pulses or “spikes”. However, eachtransient has a leading edge and a trailing edge. The leading edge whichat its peak defines the amplitude of the transient emission inherentlyoccurs as an inevitable result of the combustion process within theengine. The trailing edge exhibits a more gradual decline. The drivecycle of FIG. 1 was performed on a diesel powered vehicle with exhaustgas recirculation (EGR). Advances in the micro-processor art coupledwith known computer-based techniques such as feed forward, artificialintelligence, adaptive learning, etc., have resulted in fasterresponding EGR systems which act to dampen the trailing edge of thetransient. However, the leading edge of the transient will always occur.The expected advances in the EGR art conceivably could result in alowering of the overall NOx concentrations. However, such systems willnot replace the control system of the present invention or the need fora control method such as described herein. That is, improved EGR systemswill supplement the control method described herein to assure fullfunctionality of the SCR system using an external reductant, over theentire operating range of the engine.

[0087] 3) When the vehicle decelerates, such as at the decelerationdesignated by reference numeral 10C, the NOx emissions drop and dropbelow the NOx concentration which occurs at steady state conditions suchas indicated by the corresponding NOx emission drop shown by referencenumeral 12C in FIG. 1.

[0088] In general summary, FIG. 1 shows the NOx transient emissionscomprise a significant portion of the NOx emissions emitted by a dieselpowered vehicle during a regulated drive cycle.

[0089] As a matter of definition, and when used in this DetailedDescription and in the claims:

[0090] a) “Deceleration” means an engine operating condition whereat thevehicle motors the engine.

[0091] b) “Acceleration” encompasses a rate of change in the enginesystem which is increasing and is not limited merely to rate changes inthe engine rpm but also includes i) increases in engine load whether ornot accompanied by a change in engine speed and ii) changes in operatingparameter(s) of the total engine “system” such as for example by achange in EGR flow or composition or actuation of a turbo charger.

[0092] c) “NOx transient” means a temporary increase in NOx emissions asexplained with reference to FIG. 1, and by “definition”, occurs at anacceleration.

[0093] d) “Steady state” means constant and occurs when the engineoperating parameters or the engine “system” does not significantlychange over a discrete time period, i.e., say NOx varies ±5%.

[0094] e) “SCR” means selective catalytic reduction and includes areducing catalyst(s) which speeds or enhances a chemical reduction ofNOx by a chemical reagent.

[0095] f) “External reductant” means any reducing reagent which issupplied to the exhaust stream from a source other than the products ofcombustion produced in the combustion process of the engine. In thepreferred embodiment, the external reductant is a nitrogen based reagentsuch as ammonia metered in liquid or gaseous form to the reducingcatalyst. However, as indicated above, the control of the presentinvention is also capable of functioning with other reductants such asfuel oil.

[0096] g) “Normalized stoichiometric ratio” or “NSR” is defined as themolar quantity of reductant injected to the reducing catalyst divided bythe theoretical molar quantity of reductant which is needed tocompletely reduce NOx. Setting the NSR<1 or sub-stoichiometric is acommon practice to avoid reductant slip.

[0097] h) “Space velocity” is the volumetric flow rate of the exhaustgas at standard conditions (one atmosphere and 20° C.) divided by thevolume of the catalyst, i.e., vol of gas [m³/hr]/volume of catalyst=−1hr.⁻¹.

[0098] i) “Storage capacity” is the ability of a reducing catalyst toadsorb or store a reductant and/or NOx emissions on its surface at agiven temperature.

[0099] Referring now to FIG. 2A, there is shown a portion of a Europeansteady-state cycle (ESC), i.e., a heavy duty test. This cycle stepsthrough a series of constant load and speed combinations. These datashown were taken from a 12 liter heavy duty diesel engine which did nothave an EGR system. The catalyst system was supplied from EngelhardCorp. and included a reducing or deNox catalyst and an oxidationcatalyst. A urea external reductant was applied in a conventional mannerto be described below. Control of the reductant was by a separatemicroprocessor which control communicated with the engine control unit(ECU). The control metered the reductant in a manner designated hereinas “NOx following” which means the reductant was metered based on theactual NOx emissions emitted by the engine as predicted by conventionaltechnology using steady state NOx maps of selected engine operatingparameters and the catalyst inlet temperature. The data shown in FIG. 2Ais thus somewhat typical of what occurs in conventional controltechniques which sense the engine operating parameters to determinesteady-state NOx emissions and then meter an external reductant into theexhaust gas at an NSR ratio sufficient to cause reduction of the NOxemissions as they pass over the reducing catalyst.

[0100] In FIG. 2A several plots or traces are shown over a timed portionof an ESC cycle shown as seconds on the x-axis. The lowest most trace,designated by reference numeral 20, plots the load or torque on they-axis. It can be readily seen that the load is applied in steps withthe test including a relative high step load designated by referencenumeral 20A, followed by a series of 4 slightly varying, intermediateload steps followed by a relative low load step designated by referencenumeral 20B.

[0101] The uppermost trace of FIG. 2A is a plot of the NOx emissions inppm (parts per million) emitted for the step loads imposed on the engineshown by trace 20. The emission scale for the plot is limited to 1000ppm of NOx and the emissions produced during step load cycle 20A is “offthe graph”. The remaining trace is within the scale and basicallycorrelates the known fact that engine loadings result in NOx emissionsattributed to the load. Note that the NOx concentrations basicallycorrespond to the torque on the engine.

[0102] The middle trace of FIG. 2A is plot of the exhaust gastemperature at the inlet of the reducing catalyst designated by thetrace passing through squares and indicated as reference numeral 24 anda plot of the exhaust gas temperature at the outlet of the reducingcatalyst designated by the trace passing through circles and indicatedas reference numeral 25. Two observations should be noted. First, for“significant” step load changes, i.e., 20A and 20B, the outlettemperature of the catalyst significantly lags the inlet temperature ofthe catalyst and this lag can be hundreds of seconds. On the other handwhen the step loads do not significantly vary as shown by the mid bandportion of load trace 20, the outlet temperature follows the inlettemperature of the catalyst.

[0103] Referring now to FIG. 2B, there is shown the results of anespecially constructed step load using the same engine and reductantcontrol strategy discussed with reference to FIG. 2A. In FIG. 2B, aseries of 5 rapidly applied step loads are applied to the enginefollowed by a “no load” period as shown by the lowermost tracedesignated by reference numeral 27. The five rapidly applied step loadscan be viewed as indicative of engine loads applied as the operatorshifts the transmission of a vehicle through various gear ranges. Asexpected, the uppermost trace of FIG. 2B designated by reference numeral28 shows increase and decrease of NOx emissions corresponding to therapid changes in load trace 27.

[0104] As in FIG. 2A, the middle portion of FIG. 2B shows a plot ofexhaust gas temperature at the inlet, of the reducing catalyst passingthrough squares and designated by reference numeral 29 and a plot ofexhaust gas temperature at the outlet of reducing catalyst passingthrough circles and designated by reference numeral 30. Catalyst inletand temperature plot 29 clearly shows a rapid exhaust gas temperatureincrease during the transient NOx emission. Temperature plot 30 shows aperiodic delay or lag before the exhaust gas temperature at the outlet“catches up” to the inlet temperature. FIG. 2B shows that as a result ofchanges to the operating conditions of the engine, the catalyst inlettemperature and NOx concentration rise and fall following the change inengine operating conditions. However, a periodic time delay occursbefore the entire reducing catalyst is affected by the change in exhaustgas temperature caused by the NOx transient emission. This is admittedlydifficult to discern in the ESC step load tests illustrated in FIG. 2Aand still yet more difficult to discern in a drive cycle such as shownin FIG. 1. However, this relationship, demonstrated in the speciallyconstructed tests of FIG. 2B, forms one of the underpinnings of thepresent invention.

[0105] More specifically, a reducing catalyst, preferably one formulatedto react with a nitrogen reagent, has an ability to store and releasethe reductant and heat. The NOx emission is, for all intents andpurposes, instantaneously formed and passes through the system at thespeed of the exhaust gas. If the catalyst has sufficient storedreductant, the transient NOx emission will react with the reductant andbe reduced. The time constant for the NOx transient to pass through thecatalyst bed is much smaller (i.e., the speed of the gas) than the timeconstant for the temperature pulse to pass through the catalyst bed. Asthe temperature of the reducing catalyst increases, its ability to storereductant and NOx decreases. Conventional control systems meter thereductant on the basis of NOx emissions currently produced. FIG. 2Bclearly shows that it is not only possible but likely that any given NOxtransient can occur while the temperature of the reducing catalyst isexperiencing the after effects of a prior NOx transient and is within atemperature range whereat the reductant rate called for by the currentNOx transient can not be stored on the catalyst. The inevitable resultis reductant slip. The present invention addresses this problem, asexplained in detail below, by accounting for the ability of thecatalyst, at any given time, to store and release the reductant and NOxemissions with respect to the NOx emissions being currently produced bythe engine.

[0106] Referring now to FIG. 3, there is shown schematically theelements comprising an external reductant supplied SCR system applied toa mobile internal combustion engine 32. An intake valve 33 controlsadmission of air to the engine's combustion chamber 34 from an intakemanifold 36. An exhaust valve 37 controls the emission of exhaust gasesproduced to an exhaust manifold 38, in turn connected to an exhaust pipe39. Attached to exhaust pipe is a close-coupled catalyst 40 followed bya reducing or de-Nox catalyst 42 in turn followed by an oxidationcatalyst 43.

[0107] All catalysts shown, 40, 42, 43, are conventional. While reducingcatalyst 42 is a necessary element for the inventive system to work, itis not, per se, part of the invention. That is the inventive method andsystem does not require specially formulated catalysts to function.Reducing catalyst 42 may generally comprise a zeolite or a mixture oftitanium, vanadium, tungsten and/or molybdenum oxides and one or morereducing catalysts may be used or different catalyst bed formulationsused in one reducing catalyst. Reference may be had to Byrne U.S. Pat.No. 4,961,917 incorporated herein by reference for a description of asuitable reducing catalyst. Generally, the oxidation catalyst comprisesa support such as alumina and a precious metal such as platinum forexample. As is generally known, oxidation catalyst 43 is provided, amongother reasons, to oxidize the excess of any unreacted ammonia leavingreducing catalyst 42 with oxygen to nitrogen and water. Reference may behad to Speronello et al. U.S. Pat. Nos. 5,624,981 and 5,516,497,incorporated herein by reference, for a staged metal promoted zeolitecatalysts having a stage favoring oxidation of excess ammonia. Closecoupled catalyst 40 is designed to reduce emissions during cold startand reference may be had to Sung U.S. Pat. No. 5,948,723, incorporatedherein by reference for a description of a catalyst suitable for coldstart engine applications.

[0108] A fuel injector 45 receives pressurized fuel from a fuel tank 46for pulse metering of the fuel into combustion chamber 34. A fuel demandcommand, i.e., accelerator pedal, schematically represented by referencenumeral 48 controls fueling and consequently the speed/load of thevehicle.

[0109] In the embodiment of FIG. 3, an aqueous urea reservoir 50 storesa urea/water solution aboard the vehicle which is pumped through a pump51 including a filter and pressure regulator to a urea injector 54. Ureainjector 54 is a mixing chamber which receives pressure regulated air online 55 which is pulsed by a control valve to urea injector 54. Anatomized urea/water/air solution results which is pulse injected througha nozzle 56 into exhaust pipe 39 upstream of reducing catalyst 42.

[0110] This invention is not limited to the aqueous urea meteringarrangement shown in FIG. 3. It is contemplated that a gaseous nitrogenbased reagent will be utilized. For example, a urea or cyanuric acidprill injector can meter solid pellets of urea to a chamber heated bythe exhaust gas to gasify the solid reductant (sublimation temperaturerange of about 300 to 400° C.). Cyanuric acid will gasify to isocyanicacid (HNCO) while urea will gasify to ammonia and HNCO. With eitherreductant, a hydrolysis catalyst can be provided in the chamber and aslip stream of the exhaust gas metered into the chamber (the exhaust gascontains sufficient water vapor) to hydrolyze (temperatures of about 150to 350° C.) HNCO and produce ammonia.

[0111] In addition to urea and cyanuric acid other nitrogen basedreducing reagents or reductants especially suitable for use in thecontrol system of the present invention includes ammelide, ammeline,ammonium cyanate, biuret, isocyanic acid, melamine, tricyanourea, andmixtures of any number of these. However, the invention in a broadersense is not limited to nitrogen based reductants but can include anyreductant containing HC such as distillate fuels including alcohols,ethers, organo-nitro compounds and the like (e.g., methanol, ethanol,diethyl ether etc) and various amines and their salts (especially theircarbonates), including guanidine, methyl amine carbonate,hexamethylamine, etc.

[0112] The operation of engine 32 is under the control of an ECU (enginecontrol unit) 60. ECU 60 is a microprocessor based control systemcontaining a conventional CPU with RAM, nonvolatile RAM, ROM, look-uptables for engine mapping purposes, etc. ECU 60 receives input sensorsignal information, processes the data by programmed routines andgenerates actuator output signals. While a dedicated processor could besupplied to control the SCR system of the present invention, it is aparticular feature of the invention that the control system can functionwith existing sensors and the ECU now used to control the operation ofengine 32.

[0113] Conventional sensor input signals now processed by ECU 60 andutilized in the current control system include a speed/load signal froma speed/load pickup 61 (i.e., a speed sensor and a torque sensor such asused in the engine's transmission), a fuel demand signal fromaccelerator pedal 48, air intake temperature signal (optionally andadditionally humidity) from a temperature sensor 62, mass air flow froma pressure or air flow sensor 64 and optionally an exhaust gastemperature sensor from a temperature sensor 65 if the vehicle is soequipped. (Alternatively, exhaust gas temperature can be modeled by ECU60 from other sensors not shown such as ambient temperature, coolanttemperature, fueling signals. See the '064 patent incorporated byreference herein.) If additional sensors are to be supplied, suchsensors would take the form of a catalyst inlet exhaust gas sensor 67 oralternatively, catalyst inlet exhaust gas sensor 67 and a catalystoutlet exhaust gas sensor 68 for calculating mid-bed steady statetemperatures of reducing catalyst 42. As indicated, ECU 60 reads thesensor input signals, performs programmed routines typically involvinglook-up tables to access mapped data and generates output or actuatorsignals such as fuel injector actuator signal shown on dash line 69.Insofar as the control system of the present invention is concerned, ECU60 generates a metering signal on dash line 70 to urea injector 54.

[0114] Referring now to FIG. 4, there is shown a flow chart of thepresent control system which is conventional in the sense that engineoperating parameters are read to determine a NOx concentration ofemissions produced by the engine at engine out NOx block 75; anormalized stoichiometric ratio of reductant to NOx emissions is set atNSR block 76; a reductant rate is set based on the NSR and engine outNOx emissions at reductant calc. block 77 and urea injector 54 isinstructed at injection block 78 to meter the atomized urea/watermixture at a defined pulse based on reductant calc. block 77.

[0115] In particular, engine out NOx block 75 receives a speed signal 80and a torque signal 81 from speed/load sensor 61 at any given time andaccesses a map stored in a look up table in ECU 60 to predict for thattime the actual NOx emissions emitted by engine 34. Reference can be hadto SAE paper 921673, incorporated by reference herein, for severaltorque/speed maps. While some prior art has suggested mapping NOxtransient emissions, the suddenness of the transient coupled withvarying decay coupled further with overlapping or compound transients isbelieved to either render the mapping not feasible or the mapping wouldbe so extensive that a significant increase in memory of ECU 60 would berequired.

[0116] Within the prior art, the NSR ratio at NSR block 76 has beensimply been set at some fixed sub-stoichiometric ratio to minimizereductant slip or breakthrough. Others, recognize that competingoxidation reactions at higher catalyst temperatures (among otherreasons) adjust the NSR ratio to reflect a sub-stoichiometric NSR atcurrent catalyst temperature. Still others, additionally recognize thatthe residence time or contact time (i.e., space velocity) of thereductant with the catalyst has to be sufficient to allow the reductantto diffuse and react with the NOx but state that the system design orsystem operation is such that the residence time is not a limitingfactor. These prior art systems determine the NOx concentration(predicted open loop from steady state engine maps) and meter thereductant at a rate determined by the NSR, established in the mannerindicated, applied (i.e., multiplied) to the NOx concentration.

[0117] This invention follows a generally similar approach in that aconcentration of NOx is determined and a NSR value is applied to the NOxconcentration to determine the rate at which the reductant is meteredupstream of reducing catalyst 42. However, the NSR is extrapolated froma stored look-up table which sets a NSR value which will not produce areductant slip above a set reductant range, i.e., say. 5 ppm ammonia or3 ppm ammonia. The actual slip concentration is set at or below a or anexpected regulatory standard. An example of an NSR map used in thepresent invention and stored in a look-up table to be accessed by ECU 60is contained in FIG. 5. In FIG. 5, catalyst temperature is plotted onthe z-axis and encompasses a temperature range at which reducingcatalyst 42 can reduce NOx emissions, typically 200-400° C. butgenerally 150-600° C. The space velocity is plotted on the x-axis,typically anywhere from 5 to 60,000 hr.⁻¹, and the NSR ratio, plottedfrom a value in slight: excess of 1 to zero, (producing a reductant slipwithin a defined range) is plotted on the y-axis. Note the significantvariation in NSR as a result of variations in space velocities andcatalyst temperatures.

[0118] By way of explanation, reference can be had to an article “NOxRemoval with Combined Selective Catalytic Reduction and SelectiveNoncatalytic Reduction: Pilot-Scale Test Results” by B. Gullett, P.Groff, M. Linda Lin and J. M. Chen appearing in the October, 1994 issueof Journal of Air & Waste Management Association, pages 1188-1194′, (the“Pilot-Test Article), incorporated by reference herein and made a parthereof. The authors of the Pilot-Test Article had earlier presented apaper entitled “Pilot-Scale Testing of NOx Removal with CombinedSelective Catalytic Reduction and Selective Non-Catalytic Reduction” atthe 1993 Joint EPA/EPRI Symposium on Stationary Combustion NOx Control,Bal Harbour, Fla. (the “Paper”) also incorporated by reference hereinand made a part hereof. Both the Paper and the Pilot Test Articlediscuss an industrial NOx reduction system using a hybrid SNCR/SCRsystem which nevertheless drew several conclusions relative to the SCRsystem which have been utilized and expanded in this invention. ThePilot-Test Article recognized that space velocity is a controllingfactor but determined that space velocity did not affect the performanceof the SCR catalyst when the stoichiometric ratio of ammonia to NOx wasset at 1 or less. The Paper discussed high space velocities(encompassing velocities capable of being achieved by mobileapplications) but concluded the stoichiometric ratio was notsignificantly influenced by the high space velocities. The Pilot-TestArticle also recognized that there was an optimum temperature range forthe SNCR system. However, the article did conclude that ammonia slip canbe determined on the basis of the stoichiometric ratio of ammonia/NOxand is independent of the quantity of NOx, i.e., FIG. 7 of thePilot-Test Article. That conclusion has since been verified for mobileSCR applications to which this invention relates. However, it has beendetermined that space velocity does affect ammonia slip for any givenNSR of 1 or less as well as temperature (within the set temperaturerange). Importantly, it has been determined that a relationship existsbetween NSR, space velocity and catalyst temperature which will producea reductant slip of a set concentration. Accordingly, it is possible tomodel space velocity, catalyst temperature and NSR for any practicalslip concentration to establish a NSR value at any given sensed (ormodeled or computed) catalyst temperature and space velocity from whicha rate at which the reductant is metered can be established withoutproducing a reductant slip that exceeds a set amount. Although amathematical model could be generated, in practice, the NSR values aredetermined empirically for any given reducing catalyst and mapped asshown in FIG. 5. Establishing a range of NSR values, which issubstantially sub-stoichiometric, producing no more than a setconcentration of reductant slip as a function of space velocity andcatalyst temperature within a set range is believed different than thatused in other mobile SCR control systems and forms a part of the presentinvention. It should be understood that the invention disclosed hereinwill function using any conventional prior art system for setting theNSR. Improved results are possible using the method of establishing aNSR value vis-a-vis FIG. 5. Still further, any conventional SCR controlsystem relying on steady state conditions to establish metering of thereductant or any other system to establish the concentration of NOxemissions to be reduced, can be improved if the NSR is determined at aset slip range by modeling space velocity, catalyst temperature and NSRfor that range.

[0119] As described thus far, this method will produce very high NOxconversion efficiencies sufficient to meet increasingly stringent NOxregulations but only for steady state engine operating conditions.

[0120] For reasons discussed above with reference to FIGS. 2A and 2B,the after effects of the NOx transient are not felt until a relativelylong and variable time has elapsed. While the median temperature of thecatalyst bed defines the ability of the catalyst bed, the preciseposition in the bed at which a median temperature can be sensed changesas the effects of the transient emissions are experienced by thecatalyst. Because of the transient wave front moving through the bedeven if temperature upstream and downstream of the reducing catalyst wassimultaneously sensed and applied to some formula giving a mid-bedtemperature (for example, the temperature summed divided by two) aninstantaneous temperature indicative of the median bed temperature wouldnot result. Apart from considerations relating to the temperature of thereducing catalyst, it is generally known that conventional steady statesystems cause reductant slip on acceleration. This results because thetransient calls for a corresponding high amount of reductant while thecatalyst is partially or fully charged with stored reductant and thecatalyst bed temperature is substantially less than the inlettemperature, so that slip inevitably occurs. After the transient theengine NOx emissions drop and the steady state system calls for areduction in the reductant. However, the transient has already passedthrough the reducing catalyst and the stored reductant used so that thereducing catalyst is ready to store the reductant but the system callsfor minimum reductant.

[0121] This invention introduces a delay in the control system toaccount for the after effects of NOx transients while still allowingsteady-state control to occur. A delay is introduced in the actualemissions determined in engine out NOx block 75 by an NOx filter block90 and a delay is introduced in the catalyst temperature signal 91 (suchas sensed by temperature sensors 65, or 67, or 67 and 68, or modeledfrom engine operating parameters) by a Cat filter block 92. Each filterblock 90, 92 changes its input signal in a diminishing manner over a lagor delay period correlated to the time constant used in the filter. Inaccordance with the broader scope of the invention, a non-varying or anarbitrary time constant can be utilized for the NOx filter on the basisthat any diminishing delay of the signal is better than none. However,as will be explained, a particularly important feature of the inventionis that the NOx filter employs a varying time constant correlated to thecapacity of the catalyst to reduce NOx emissions at a given temperature.

[0122] NOx calculated filter 90 is a second order filter which isdesigned to make use of the NH3 storage capabilities of the SCR systemat low temperature and to improve urea hydrolysis, as well. The timeconstant for this second filter is extrapolated from a look-up tablecorrelating the capacity of the catalyst to store reductant at a giventemperature as explained further below.

[0123] The theory behind the second order NOx filter is as follows. Twoconsiderations are important: a) NH₃ storage in the catalyst increaseswith decreasing catalyst temperature, and b) hydrolysis reaction (ureasolution -> NH₃ molecules) improves with decreasing space velocity.

[0124] Considering actual (engine out NOx block 75) and filtered (NOxfilter block 90) NOx signals during a step load cycle, for example, thefiltered NO_(x) signal is smoother. This also leads to a smootherinjection profile. When taking-off engine load the filtered signal fallsdown slower than the actual NOx. At the same time the space velocity islow, so a high NSR value will be taken from the NSR look-up table. Thisprovides the opportunity to inject additional urea under“hydrolysis-friendly” conditions. The additional urea quantity islimited by the storage capacity of the catalyst in turn correlated tothe catalyst temperature and space velocity of the exhaust gas.Therefore, a filter dependent on such correlation is introduced.

[0125] This filter comprises two first order filters in series with bothtime constants being a function of the catalyst capacity at any givencatalyst functional temperature. In other words the time constants areequal to each other and are variable. The value is obtained from alook-up table which has a functional catalyst temperature as input andfrom which a time constant related to the capacity of the storereductant at that temperature is established as an output. In thecontinuous time domain the filter (two first order filters in series)can be represented by the transfer function [ratio of the transform ofthe output variable NOx_(Filt), (NOx filter block 90) to the transformof the input variable NOx_(EngOut) (engine out NOx block 75)] shown asequation 1: Equation  1:${H_{NOx}(s)} = {\frac{{NOx}_{Filt}}{{NOx}_{EngOut}} = {\frac{1}{{\tau_{NOx1} \cdot s} + 1} \cdot \frac{1}{{\tau_{NOx2} \cdot s} + 1}}}$

[0126] and

τNOx1=τNOx2=f(Cat)

[0127] where:

[0128] NOx_(EngOut)=Predicted engine out NOx (from map, block 75)

[0129] NOx_(Filt)=Filtered NOx

[0130] τ_(NOx1), τ_(NOx2)=Time constant—function of catalyst temperaturecorrelated to capacity of catalyst to store reductant and NOx

[0131] s=differential operator (continuous domain)

[0132] note:

[0133] “H _(NOx) (s)” is a general representation of a transferfunction, “H”. The “NOx” subscript indicates the process and the “(s)”points out that it is a continuous process. The form “s” should berecognized as a differentiation term which means that the correction tothe input occurs only during changing or transient conditions.

[0134] However this equation is implemented in a controller which meansthat this formula has been put in a discreet form, i.e., differenceequations. In a discreet form the first, first order filter may berepresented by equation 2: $\begin{matrix}{{{NOx}_{Filt1}(n)} = {\frac{{{NOx}_{EngOut}(n)} - {{NOx}_{Filt1}\left( {n - 1} \right)}}{\tau_{NOx1}} + {{NOx}_{Filt1}\left( {n - 1} \right)}}} & {{Equation}\quad 2}\end{matrix}$

[0135] But because two first order filters have been placed in series,the actual filtered NOx value is the result of the second first orderfilter, which in discreet formula may be represented by differenceequation 3: $\begin{matrix}{{{NOx}_{Filt2}(n)} = {\frac{{{NOx}_{Filt1}(n)} - {{NOx}_{Filt2}\left( {n - 1} \right)}}{\tau_{Nox2}} + {{NOx}_{Filt2}\left( {n - 1} \right)}}} & {{Equation}\quad 3}\end{matrix}$

[0136] and

τNOx1=τNOx2=f(Cat)

[0137] where:

[0138] NOx_(EngOut)=Predicted engine out NOx (block 75);

[0139] NOx_(Filt1)=NOx value after first filter, intermediate value;

[0140] NOx_(Filt2)=NOx value after second filter, final filtered NOxvalue;

[0141] τ_(NOx1), τ_(NOx2)=Time constant, function of catalyst capacityat predicted temperature.

[0142] Note:

[0143] The subscripts “Filt1” and “Filt2” indicate values of the firstor second first order filter. The subscript “(n)” indicates the value ofthe current sample. The subscript “(n−1)” indicates the value of theprevious sample. The output of Equation 2 is substituted for the inputin Equation 3. The time interval at which samples n are taken can bearbitrarily set or is a function of the speed of the processor at itcompletes a loop through the programmed routine. In the preferredembodiment, the time interval at which the algorithm is performed is setnear to the operating speed of ECU 60.

[0144] Reference can be had, by way of further explanation, to FIG. 6which shows NOx filter block 90 in discrete form comprising a first 1storder filter 90A corresponding to equation 2 and a second 1st orderfilter 90B corresponding to equation 3. Input to first 1st order filter90A is the output from engine out NOx block 75 and a time constant shownas τNOx on line 84. Output from first 1st order filter 90A is fed asinput on line 85 as is time constant τNOx to second 1st order filter90B.

[0145] Those skilled in the art will recognize that the invention in itsdiscrete form is not limited to equations 2 and/or 3 but can encompassany number of conventional first order filters. Reference can be had toFIG. 7A which in schematic form represents a first order filter of thetype defined by equations 2 and/or 3. By way of explanation relative toNOx filter 90, input designated “x” in first calculation block 82 isτNOx, τ, and actual emissions from engine out NOx block 75, μ₁. Feedbackis μ₂. An integration block 83 performs a conversion factor from thenumber of samples to time (i.e., seconds). Reference should be had toFIG. 7B which shows an alternate discreet 1st order filter, employingthe same terminology and reference numerals. The functioning of bothfirst order filters is generally shown in FIG. 7C in which the input isrepresented by line designated 87, generally indicative of a step load.The output of 1st order filter shown in FIG. 7A is designated byreference numeral 7A and output of 1st order filter shown in FIG. 7B isdesignated by reference numeral 7B.

[0146] Reference can now be had to FIG. 8 which is an input/output graphdepicting the various filter concepts falling within the broader scopeof the invention. Limiting discussion to NOx filter 90 (althoughapplicable to Cat filter 92), an input indicative of a step load(discussed with reference to FIG. 2) is shown by the straight lineindicated by reference numeral 93. The y-axis can be viewed as NOxconcentrations and the x-axis time so input 93 is the actualconcentrations of NOx produced by the engine as predicted from look-upmaps at engine out block 75. Again, NOx filter block 90 can take, inaccordance with broader aspects of the invention, various forms. Afilter based on a moving average as discussed above is represented bydash line 94 and clearly shows a change in the concentration of thepredicted actual emissions over a lag period which change diminishesover the filter delay period. A first order filter, only, such as shownin FIGS. 7A and 7B is shown by the output curve passing through squaresand designated by reference numeral 95. The preferred second orderfilter is shown by the output curve passing through circles anddesignated by reference numeral 96. As will be explained below, the NOxtime constant for all filters, is determined by a look-up table whichestablishes, for various temperatures of any specific catalyst, a timeconstant indicative of the time response of the catalyst to storereductant and NOx emissions as a function of the capacity of thecatalyst.

[0147] As can be seen in FIG. 8 the load increase and the load decreaseis delayed. A delay in adding the reductant at the onset of thetransient reduces the likelihood of reductant slip. A delay inrecognizing a decrease in NOx emissions results in an increase inreductant but at a condition, i.e., lower exhaust speed and temperature,whereat the hydrolysis reaction is more likely to proceed to completionand the reducing catalyst storage capacity is increased.

[0148] Referring still to FIG. 4, a filter is applied to determine thetemperature of reducing catalyst 42 in order to account for the changingtemperature of the catalyst associated with the NOx transient emission.The exhaust gas velocity on input 98 such as determined by air mass flowor pressure sensor 64 is converted to a current time space velocity atspace velocity block 99. Space velocity output as shown is to NSRcalculation block 76 per the map as discussed above relative to FIG. 5.However, the space velocity is also used to filter the catalysttemperature.

[0149] Conceptually, the catalyst temperature prediction can be effectedby use of a running average of a measured exhaust gas which conceptuallycan be either post or pre catalyst. The number of samples of temperaturetaken from which the average catalyst temperature would be determinedwould then depend on the value of the space velocity. The reasoningbehind this concept was that with a step load increase or decrease aheat or cold front, respectively, moves through the catalyst. The speedat which this front proceeds through the catalyst is space velocitydependent.

[0150] While in accordance with the broader concepts of the invention, amoving average for the catalyst mid-bed temperature can be used (as wellas a moving average for calculated NOx emissions with the number ofsamples, dependent on the storage capacity of the catalyst at itscurrent mid-bed temperature), it is a specific aspect of the inventionthat a second order filter can be used to predict catalyst temperaturebecause, among other reasons, the second order filter is far more easierto implement than a mathematical technique to determine a moving averageover a varying time integral which may be significantly long induration. Again the implementation includes two first order filters inseries with variable time constants. The time constants are a functionof the space velocity through the catalyst. In transfer function form,the filter can be defined by equation 4: $\begin{matrix}{{H_{TCat}(s)} = {\frac{{TCat}_{Filt}}{TExhaust} = {\frac{1}{{\tau_{Cat1} \cdot s} + 1} \cdot \frac{1}{{\tau_{Cat2} \cdot s} + 1}}}} & {{Equation}\quad 4}\end{matrix}$

[0151] and

τCat1=τCat2=f(SV)

[0152] where:

[0153] TCat_(Filt)=Predicted catalyst temperature;

[0154] TExhaust=is the measured exhaust gas temperature upstream of thecatalyst;

[0155] τ_(Cat1), τ_(Cat2)=Time constant which is a function of the spacevelocity;

[0156] s=differential operator (continuous domain)

[0157] note:

[0158] “H _(TCat) (s)” is a general representation of a transferfunction, “H”. The “TCat” subscript indicates the process and the “(s)”points out that it is a continuous process. Again, the form “s” shouldbe recognized as a differentiation term which means that the correctionto the input occurs only during changing or transient conditions.

[0159] Again this equation is implemented in a controller which meansthat this formula has been put in a discreet form. In a discreet formthe first, first order filter may be defined by equation 5:$\begin{matrix}{{{TCat}_{Filt1}(n)} = {\frac{{{TExhaust}(n)} - {{TCat}_{Filt1}\left( {n - 1} \right)}}{\tau_{Cat1}} + {{TCat}_{Filt1}\left( {n - 1} \right)}}} & {{Equation}\quad 5}\end{matrix}$

[0160] But because two first order filters have been placed in series inorder to create a second order filter, the actual filtered catalysttemperature is the result of the second first order filter, as shown bydiscreet or difference equation 6: $\begin{matrix}{{{TCat}_{Filt2}(n)} = {\frac{{{TCat}_{Filt1}(n)} - {{TCat}_{Filt2}\left( {n - 1} \right)}}{\tau_{Cat2}} + {{TCat}_{Filt2}\left( {n - 1} \right)}}} & {{Equation}\quad 6}\end{matrix}$

[0161] and

τCat1=τCat2=f(SV)

[0162] where:

[0163] TExhaust=Measured exhaust temperature upstream of the catalyst;

[0164] TCat_(Filt1)=Catalyst temperature after first filter,intermediate temperature;

[0165] TCat_(Filt2)=Predicted catalyst temperature, final filteredtemperature;

[0166] τ_(Cat1), τ_(Cat2)=Time constant which is a function of the spacevelocity.

[0167] note:

[0168] The subscripts “Filt1” and “Filt2” indicate values of the firstor second first order filter. The subscript “(n)” indicates the value ofthe current sample. The subscript “(n−1)” indicates the value of theprevious sample.

[0169] The time constant for the catalyst, τCAT, is constantly varying(straight line) indicated schematically by the graph shown in FIG. 4designated by reference numeral 97 and generally determined inaccordance with equation 8 as follows: $\begin{matrix}{\tau_{CAT} = \frac{M_{CAT} \cdot {Cp}_{CAT}}{{SV} \cdot P_{GAS} \cdot {Cp}_{GAS} \cdot V_{CAT}}} & {{Equation}\quad 7}\end{matrix}$

[0170] where

[0171] M is the mass of the catalyst;

[0172] V is the volume of the catalyst;

[0173] Cp_(CAT) is the heat capacity of the catalyst;

[0174] P_(GAS) is the density of exhaust gas;

[0175] Cp_(GAS) is the heat capacity of the exhaust gas; and,

[0176] SV is the space velocity of exhaust gas.

[0177] Equations 6 and 7 provide a method to determine in real time thetemperature of the reducing catalyst accounting for the temperaturechange attributed to NOx transient emissions.

[0178] While it is a necessary element of the present invention, thedetermination of the catalyst temperature by a filter using a spacevelocity time constant, τCat, may be used in other emission controlsystems or for other emission related functions. Although a thermocouplecan directly measure temperature, the life of a thermocouple in avehicular environment is limited. More importantly, a moving heat wavefront(s) resulting from a NOx transient emission(s) does not uniformlydissipate its heat to the catalyst bed. A precise position can not beestablished for all the transients whereat a maxima or average heatfront will occur. Generally, a mid-bed temperature is necessary toestablish an accurate NSR but the wave front position is variable andnot strictly speaking at the exact mid-point of the catalyst. Whileinlet and outlet exhaust gas temperature sensors 67, 68 can givereadings with difference divided by a constant, i.e., two, to give amid-bed approximation, significantly more accurate results are obtainedif the catalyst temperature (½ the sum of inlet and outlet temperatures)is filtered by the τCat constant to account for the changing nature ofthe heat wave front passing through the catalyst. In fact, τCat has beenfound to accurately predict catalyst temperatures using only the exhausttemperature at inlet sensor 67 or exhaust manifold sensor 65 (or even amodeled exhaust gas temperature from ECU 60). As used herein and in theclaims, reference to catalyst functional or functioning temperaturesmeans the mean or median temperature of the reducing catalyst bed. Thecatalyst filter using a τCat constant to modify precatalyst exhaust gastemperature produces a more accurate functional catalyst temperatureaccounting for transient emission heat wave fronts than other knownmethods. In support of this, reference should be had to FIG. 9 which isa graph of catalyst temperatures taken during an ETC (European transientcycle) test. The trace passing through diamonds and designated byreference numeral 87 is the average catalyst temperature recorded byinlet and outlet sensors 67, 68. It should be recalled that FIG. 2B (and2A) plotted the inlet and outlet temperatures separately. The inlettemperature oscillated significantly and the outlet temperature was“damped”. Neither inlet nor inlet temperature readings can account forthe catalyst temperature when affected by transient emissions. Averagecatalyst temperature trace 87, as expected, dampens the inlettemperature oscillations. However, the oscillations are still presentand demonstrate why actual temperature measurements are not suitable fora reductant metering system. The mid-bed temperature was measured duringthe ETC test and is plotted as the trace passing through squaresdesignated by reference numeral 88 in FIG. 7. The mid-bed temperaturedoes not have the oscillations associated with the exhaust gas, and asexpected, has a wave form shape. The predicted temperature, determinedby τCat, is shown by the trace passing through circles designated byreference numeral 89. The predicted temperature was based on sensingexhaust gas temperature only. Predicted temperature trace 89 followsmid-bed temperature trace 88 and clearly demonstrates why it is asuperior tool, easily implemented in any control system withoutintensive heat transfer calculations to determine the functionalcatalyst temperature.

[0179] A particularly novel feature of this filter is that during ashort engine stop the filter predicts the catalyst temperature accordingto the cooling down process. This is done by splitting the two firstorder filters in series into two individual parallel operating firstorder filters and feeding the ambient temperature into both filters asinput. The output of the filters represents the predicted catalysttemperature. The reason that the combined filters are split is because acooling down curve of a catalyst can be represented very well by a firstorder filter with a variable time constant. The time constant iscomputed from a look-up table which has as input, e.g., a timer or thedifference in predicted catalyst temperature and ambient temperature.The transfer function in continuous form for this filter is representedby equation 8: $\begin{matrix}{{H\quad {\tau_{Cool}(s)}} = {\frac{T_{Cool}}{T_{Amb}} = \frac{1}{{\tau_{{{Cool}\quad 1},2} \cdot s} + 1}}} & {{Equation}\quad 8}\end{matrix}$

[0180] and

τCool1=τCool2=f(Timer)

[0181] where:

[0182] TAmb=Ambient temperature

[0183] TCool=Catalyst temperature while cooling down

[0184] τ_(Cool1), τ_(Cool2)=Time constant which is a function of time,e.g., timer or temperature difference

[0185] Reference should be had to FIG. 10 which shows in schematic,conceptual form, how the cool down filter can be implemented in Catfilter block 92. A switching arrangement is shown to switch the filtersfrom a series arrangement to a parallel arrangement. The filter is shownswitched into its series arrangement and operates with τCat and exhaustgas temperature inputs to the first 1st order filter 92A and then to thesecond 1st order filter 92B in the same manner as explained withreference to FIG. 6. On engine shut down, switch line 103 actuates theswitches to the position shown by the dotted lines. Switching inputsτCool and ambient temperature on line 104 to second 1st order filter 92Bto predict the cool down temperature of the catalyst used upon enginerestart.

[0186] The reason for feeding the second parallel placed filter with thesame information as well is to keep this filter (i.e., first 1st orderfilter 92A) from freezing or drifting to faulty values when the engineis started again after a short stop. On restart, the filters areconnected again in series and both have to start from the same values inorder to predict accurately the catalyst temperature again based on themeasured value.

[0187] The advantage of using the temperature difference betweencomputed catalyst temperature and ambient temperature for determinationof the time constant is that no counters are required which have to havea capacity for dealing with “large” times.

[0188] This feature is not only very useful during testing but also inpractice when a vehicle has made a short stop (refueling, etc.). Thesoftware is not starting from a default (reset) value. Starting from adefault value while the catalyst is hot means that urea is not injectedat the earliest possible moment, which means lower conversions.

[0189] The above representation of the catalyst temperature filters isfor the continuous domain. However they are implemented in discreet formin the controller by difference equation 9 as follows: $\begin{matrix}{{TCool}_{{{Filt}\quad 1},2} = {\frac{{{TAmb}(n)} - {{TCool}_{{{Filt}\quad 1},2}\left( {n - 1} \right)}}{\tau_{{{Cool}\quad 1},2}} + {{TCool}_{{{Filt}\quad 1},2}\left( {n - 1} \right)}}} & {{Equation}\quad 9}\end{matrix}$

[0190] and

τCool1=τCool2=f(Timer)

[0191] where:

[0192] TAmb=Ambient temperature;

[0193] TCool_(Filt1,2)=Predicted catalyst temperature while coolingdown, both filters;

[0194] τ_(Cool1)=τ_(Cool2)=Time constant which is a function of e.g.timer or temperature difference

[0195] note:

[0196] The subscript “Filt1,2” indicate values of parallel operatingfirst and second first order filter. The subscript “(n)” indicates thevalue of the current sample. The subscript “(n−1)” indicates the valueof the previous sample.

[0197] It is to be appreciated that the use of a first order filter topredict the cool down temperature of the catalyst after engine shut-offis a feature that can be implemented in any emission system whether ornot a functional catalyst temperature is obtained by the invention. Insuch application only a first order filter is used to generate a cooldown temperature of the catalyst and the cool down temperature can beused for any purpose needed by the system. The cooled own time constant,τCool, would still be generated by a look-up table either a timingconstant based on catalyst temperature on shut down or a table based onthe difference between catalyst temperature at shut down compared toambient temperature. The catalyst temperature would be the temperaturecalculated by the system using the cool down filter. In its broaderinventive scope, the cool down filter is not limited to a reducingcatalyst. For example, a hybrid vehicle employing an engine whichintermittently shuts off and on, could use a catalyst temperature forfueling control which can be easily attained by the first order cooldown filter.

[0198] The NOx filter constant, τNOx, is specific to the reducingcatalyst used in the SCR system. It is determined as a function of theability of any specific reducing catalyst to store (and release)reductant at any given temperature (within the reductant storagetemperature range of the reducing catalyst). Preferably, the NOx filterconstant is determined as a function of the ability of any specificreducing catalyst to store the external reductant and NOx emissions(within the catalyst temperature range).

[0199] Reference should be had to FIG. 11 which is a graph of the τNOxtime constant for various functional catalyst temperatures (asdetermined from Cat filter block 92) of a specific reducing catalyst 42.Catalyst functional temperature is plotted on the x-axis and τNOx isplotted as a time constant on the y-axis. The plotted time constant wasestablished through a series of tests. The catalyst was purged of anyreductant and heated to a temperature within the known catalyst storagerange (about 200 to 400° C.). An inert gas with a set concentration ofreductant was metered through the catalyst and gas samples taken at timeincrements. When the gas samples showed a reductant concentrationapproximately equal to that metered into the reducing catalyst, astorage time was established and plotted on the y-axis for thattemperature. The resulting plot designated by reference numeral 100 isthen stored in a look-up table within ECU 60. What this procedure didwas to relate the storage capacity of the catalyst to a time periodwhich time period varies with the temperature of the catalyst and isused to set the time constant τNOx for the NOx filter.

[0200] The time period while relative in the sense of an absolute timequantity affords a consistent basis for establishing the time constantfor all catalysts because a catalyst having a greater capacity to storereductant than another catalyst will, for any given temperature, take alonger time before it stops storing reductant (metered at a setconcentration rate) than a catalyst having less storage capacity. Bycorrelating the catalyst storage capacity to a storage time, a basisexists for determining the timeliness of the catalyst to react tochanges in NOx emission concentrations. All that is needed is todetermine the change in emissions because the catalyst behavior inresponse to the change can be predicted. The control system does nothave to monitor operating parameters to ascertain how the catalyst isresponding in real time to the changes nor perform any number ofintensive calculations based on the catalyst response (in the endcorrelated to the capacity of the catalyst) to adjust the reductantdosage.

[0201] While sufficient tests have not been conducted as of the date ofthis application, it is believed that data taken from a number of τNOxcurves generated from different reducing catalysts will establish acorrelation between the number and strength of storage/release sites onthe surface area of the reducing catalyst and the τNOx curve for thatspecific reducing catalyst. In the preferred ammonia reductantembodiment, the reducing catalyst can be formulated to produce, per unitarea, a mean number of Bronsted acid sites having a mean bond strengthat which ammonia molecules attach. The τNOx curve is then generated forthe formulated washcoat with known reactivity on the basis of thesurface area of the catalyst i.e., the larger the surface area, thelonger time or larger τNOx constants. Because the τNOx curve is selectedto match the transient emissions generated by any given engine, a methodfor determining catalyst sizing matched to a specific engine isestablished. Catalyst cost is minimized while NOx regulations are met.

[0202] It is also known that reducing catalysts (particularly zeolites)similarly have a varying affinity to store (and release) NOx emissionsdepending on the temperature of the catalysts. The inventioncontemplates producing a more accurate τNOx constant by accounting forthe NOx storage capacity of the reducing catalyst in a manner similar tothat explained above which determined and measured the reductant storagecapacity of the reducing catalyst. The τNOx constant is thus establishedon the capacity of any given reducing catalyst to store the reductantand NOx.

[0203] The inventive method as thus described senses exhaust gasvelocity at input 98 to produce a space velocity signal at spacevelocity block 99 which is inputted to NSR block 76. Space velocitysignal is also used to access a catalyst time constant in τCat look uptable 101 which time constant is inputted to Cat filter block 92 togenerate a functional catalyst temperature, adjusted for NOx transients,which is inputted to NSR block 76 for determining a NSR ratio pursuantto the map of FIG. 5. The catalyst temperature is also used to access aNOx time constant, in a τNOx look up table 102, which is inputted to NOxfilter block 90 to generate a calculated NOx emission concentrationwhich accounts for the transient NOx emissions produced by engine 32.The NSR ratio and calculated or filtered NOx emissions are inputted toReductant calc block 77 which determine the concentration of reductantto be injected upstream of reducing catalyst 42 at injection block 78which controls pulse metering of the reductant. Note that all majorsystem components, NOx, temperature, NSR and reductant calculation haveall been adjusted for the effects attributed to transient emissions.

[0204] It should be apparent that the inventive system, is matching thedelay experienced in real life from sudden changes in engine operatingconditions on the ability of the reducing catalyst to reduce NOxemissions by delaying the impact of the NOx emissions which wouldotherwise be sensed and used to control reductant metering. The delay isa relative but consistent number, τNox, in the sense that it is based onthe relative ability of the catalyst to reduce NOx emissions (i.e.,storage capacity) at varying temperatures. Further the catalysttemperature is a real time prediction based on the delay of the catalystto experience the changing exhaust gas wave front. The metering is setin accordance with a varying NSR (predicted current functional catalysttemperature and current space velocity). The system thus accounts fortransient emissions by emulating the effects of the transient emission,temperature and NOx, without any attempt to measure catalyst performancefollowed by an adjustment of reductant metering rate such as disclosed,for example, in the '186 patent.

[0205] As described, the control system is fully functional. There arehowever several enhancements, additions or modifications which can bemade to the control system to improve its overall operation. Inparticular a rate of temperature change control shown as dT/dt block 110can be incorporated into the system. While the algorithms discussedabove inherently account for increasing/decreasing values in the senseof positive and negative numbers, a time derivative of catalysttemperature can establish, over longer time periods, a decreasing orincreasing temperature change attributed to NOx transients. When anddepending on the rate of temperature change determined by dT/dt block110, a variable constant can be applied to the τNOx constant on adecrease in temperature rate allowing asymmetric τNOx constants forincreasing and decreasing NOx emission rates. Further, dT/dt block 110can sense a deceleration and stop reductant metering at block 77 when adeceleration occurs. In this regard, it should be recognized that whenthe catalyst temperature is below the catalyst range (i.e., less than150° C.) there is no reductant metering. There is no reductant meteringupon a vehicle deceleration. Also, when the catalyst temperature isabove the catalyst temperature range (i.e. greater than about 400° C.),the reductant is metered at a rate equal to the actual NOx emissionsproduced as determined by engine out NOx block 75. At such highertemperature the NOx time constant, τNOx, has a value of 1. Again, it isto be noted that the NOx filter is operating during changing conditionswithin a set temperature range whereat the catalyst has ability to storereductant. The fact that the filtered NOx emissions used to setreductant dosage in this range may, on acceleration, be less than enginebut emissions has no bearing on the reduction of the NOx transient buthas a bearing on reductant slip.

[0206] The system can also account for catalyst ageing by inputting anageing factor at input 111 to the NSR signal generated at NSR block 76.The ageing signal may be accessed from a look up table which correlateseither engine hours of operation or miles driven taken from vehiclesensors to an ageing factor which modifies the NSR ratio.

[0207] If time responsive, commercially acceptable NOx sensors aredeveloped suitable for vehicle application, these NOx sensors would beused in place of steady state engine maps to determine the actualconcentration of NOx emissions at engine out NOx block 75. If timeresponsive, commercially acceptable reductant, i.e., ammonia, sensorsare developed, these sensors would be used to trim the reductant signalat reductant calculation block 77.

[0208] The system can also include provision for on board diagnostics(OBD) which can be implemented, for example, by a NOx or reductantsensor downstream of reducing catalyst 42. As discussed above, currentNOx and/or ammonia sensors do not have adequate response times forcontrol of a mobile IC application. They are satisfactory for diagnosticpurposes however.

[0209] Reference can be made to FIG. 12 which shows two traces ofreductant slip (ammonia) recorded over an ETC drive cycle with thereductant metered to the SCR system with and without the control systemof the present invention. Examination of FIG. 12 shows that containedwithin an outer trace 120 is an inner trace 121. Outer trace 120represents a conventional metering control referred to as “NOxfollowing” in describing FIG. 2A, i.e., reductant metered on the basisof actual predicted actual NOx emissions emitted by the engine asdetermined by steady state NOx emission maps from engine operatingparameters and catalyst temperature. The inner trace 121 plots thereductant slip when the same engine is operated under the control systemfor the ETC cycle. In all cases the reductant slip is reduced fortransient emissions. In the tests conducted when data for inner trace121 was gathered, the system was not equipped with the dT/dtdifferential temperature change block 110 to determine decelerations.Based on a review of the slip data it is believed that if dT/dt block110 was implemented in the control to stop reductant metering duringvehicle decelerations, a further significant reduction in slip wouldoccur.

[0210] The invention has been described with reference to a preferredand alternative embodiments of the invention. Modifications andalterations to the invention will occur to those skilled in the art uponreading and understanding the Detailed Description of the Invention setforth herein. It is intended to include all such modifications andalterations insofar as they come within the scope of the presentinvention.

Having thus defined the invention, it is claimed: 1) A method forreducing NOx emissions produced in mobile internal combustion engineapplications by an external reductant supplied to an SCR system having areducing catalyst comprising the steps of: a) sensing one or more engineoperating parameters to predict a concentration of NOx emissionsindicative of the actual quantity of NOx emissions produced by theengine; b) when the actual concentration of NOx emissions changes andthe temperature of said reducing catalyst is within a set range, varyingthe actual concentration of NOx emissions, by a time constant to producea calculated concentration of NOx emissions different than the actualconcentration of NOx emissions; and, c) metering the external reductantto the reducing catalyst in said SCR system at a rate sufficient tocause the reducing catalyst to reduce said calculated concentration ofNOx emissions whereby metering of the reductant accounts for the effectson said SCR system attributed to transient NOx emissions. 2) The methodof claim 1 wherein when said actual NOx emissions increase, said timeconstant results in a calculated NOx emission concentration which isless than the increased actual NOx emissions produced by said internalcombustion engine. 3) The method of claim 2 wherein when said actual NOxemissions decrease, said time constant results in a calculated NOxemission concentration which is greater than the decreased actual NOxemissions produced by said internal combustion engine. 4) The method ofclaim 3 wherein said time constant corresponds to the capacity of anygiven reducing catalyst to at least store the external reductant at saidgiven reducing catalyst's current temperature and varies for differentcatalyst temperatures within a set temperature range. 5) The method ofclaim 4 wherein the change in actual emissions is positively determinedto be increasing or decreasing by considering the rate of change of thetemperature of the catalyst with respect to time according to therelationship dT/dt where T is the reducing catalyst temperature and t istime. 6) The method of claim 1 further including the step of ceasingreductant metering when the temperature of said reducing catalyst isbelow said range or when the engine is decelerating. 7) The method ofclaim 1 wherein said time constant is a variable correlated to the timeany given catalyst can store and/or release a given quantity ofreductant at a given catalyst temperature within said set catalysttemperature range, said storage time decreasing as said catalysttemperature increases within said set temperature range. 8) The methodof claim 7 wherein said reductant is ammonia and the storage and releasecapacity of said reducing catalyst includes the surface area of saidcatalyst over which said exhaust gases flow and the number and strengthof ammonia adsorption/absorption sites on said surface area. 9) Themethod of claim 8 wherein said storage capacity of said catalyst alsoincludes the ability of said catalyst to store NOx at a giventemperature within said catalyst temperature range. 10) The method ofclaim 1 wherein said time constant is implemented through an NOx filter.11) The method of claim 10 wherein said NOx filter includes two firstorder filters in series with one another. 12) The method of claim 10wherein said NOx filter in a continuous time domain filters the actualconcentration of NOx emissions in accordance with the transfer function${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

where τ₁ equals τ₂ and is a function of the operation of said reducingcatalyst. 13) The method of claim 12 wherein is a function of thetemperature of said reducing catalyst correlated to the capacity of saidreducing catalyst to at least store said reductant at said catalysttemperature and designated τ_(NOX). 14) The method of claim 13 whereinsaid NOx filter is in discreet form and implemented by a microprocessor,said NOx filter in said discrete form including two first order filtersin series with one another. 15) The method of claim 14 wherein the firstNOx filter in discrete form is represented by difference equation${{NOx}_{Filt1}(n)} = {\frac{{{NOx}_{EngOut}(n)} - {{NOx}_{Filt1}\left( {n - 1} \right)}}{{\tau \quad}_{NOx1}} + {{NOx}_{Filt1}\left( {n - 1} \right)}}$

and the second NOx filter in discrete form is represented by differenceequation${{NOx}_{Filt2}(n)} = {\frac{{{NOx}_{Filt1}(n)} - {{NOx}_{Filt2}\left( {n - 1} \right)}}{\tau_{NOx2}} + {{NOx}_{Filt2}\left( {n - 1} \right)}}$

where τ_(NOx1) equals τ_(NOx2); NOx_(EngOut) is said actual NOxemissions; NOx_(Filt1) is the NOx value after said first filter and isan intermediate value, and NOx_(Filt2) is said calculated NOx emissions.16) The method of claim 13 further including the step of determining thetemperature of said reducing catalyst by sensing or calculating thetemperature of the exhaust gas and filtering the temperature of theexhaust gas by a catalyst temperature filter as a function of thechanging space velocity of the exhaust gas to establish a functionalcatalyst temperature, said functional catalyst temperature used todetermine said calculated concentration of NOx emissions. 17) The methodof claim 16 wherein said catalyst temperature filter in the continuoustime domain is represented by the transfer function${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

where τ₁ equals τ₂ and is a function of the space velocity of theexhaust gases. 18) The method of claim 17 wherein said catalysttemperature filter is in discreet form and implemented by amicroprocessor, said filter in said discrete form including two firstorder filters in series with one another. 19) The method of claim 18wherein the first catalyst filter in discrete form is represented bydifference equation${{TCat}_{Filt1}(n)} = {\frac{{{TExhaust}(n)} - {{TCat}_{Filt1}\left( {n - 1} \right)}}{\tau_{Cat1}} + {{TCat}_{Filt1}\left( {n - 1} \right)}}$

and the second catalyst filter in discrete form is represented bydifference equation${{TCat}_{Filt12}(n)} = {\frac{{{TCat}_{Filt1}(n)} - {{TCat}_{Filt2}\left( {n - 1} \right)}}{\tau_{Cat2}} + {{TCat}_{Filt2}\left( {n - 1} \right)}}$

where τ_(CAT1) equals τ_(CAT2); TExhaust is said exhaust gastemperature; TCat_(Filt1) is the catalyst temperature after firstfilter, intermediate temperature and TCat_(Filt2) is said functionalcatalyst temperature. 20) The method of claim 19 wherein$\tau_{CAT} = \frac{M_{CAT} \cdot {Cp}_{CAT}}{{SV} \cdot P_{GAS} \cdot {Cp}_{GAS} \cdot V_{CAT}}$

where M is the mass of the catalyst; V is the volume of the catalyst;Cp_(CAT) is the heat capacity of the catalyst; P_(GAS) is the density ofexhaust gas; Cp_(GAS) is the heat capacity of the exhaust gas; and, SVis the space velocity of exhaust gas. 21) The method of claim 18 furtherincluding the steps of sensing ambient temperature and upon shut down ofthe engine in said mobile application, filtering said functionalcatalyst temperature by the effect of said ambient temperature as afunction of the time said engine has been shut down to determine afunctional cool down catalyst temperature and using said cool downtemperature as said functional catalyst temperature upon restart of saidengine. 22) The method of claim 21 wherein said step of filtering saidfunctional catalyst temperature to produce said cool down catalysttemperature is represented by a first order cool down filter, said cooldown filter implemented in the continuous time domain by the transferfunction ${H(s)} = \frac{1}{{\tau \cdot s} + 1}$

where τ is a function of time such as implemented by a timer or thedifference between ambient and catalyst temperature at shut down. 23)The method of claim 22 wherein said cool down filter is implemented in adiscrete form by said microprocessor. 24) The method of claim 23 whereinsaid cool down filter is effected in said catalyst filter by switchingsaid first and second catalyst filters into a parallel arrangement uponshut down of said engine and switching said first and second catalystfilters back to said series relationship upon engine start. 25) Themethod of claim 24 wherein said cool down filter in discrete form isrepresented by the difference equation${TCool}_{{Filt1},2} = {\frac{{{TAmb}(n)} - {{TCool}_{{Filt1},2}\left( {n - 1} \right)}}{\tau_{{Cool1},2}} + {{TCool}_{{Filt1},2}\left( {n - 1} \right)}}$

where TAmb is said ambient temperature; TCool_(Filt1,2) is said cooldown catalyst temperature while cooling down for both filters, andτ_(Cool1)=τ_(Cool2) and is a time constant which is a function of timeat the catalyst shut down temperature such as that recorded by a timeror is established as a time constant as a function of the differencebetween ambient and catalyst shut down temperature. 26) The method ofclaim 16 further including the step of determining a normalizedstoichiometric ratio (NSR) of reductant to NOx at which ratio a setquantity of reductant is to be injected into the exhaust stream for aset quantity of NOx emissions and factoring said calculated NOxemissions by said NSR to determine the rate at which said externalreductant is to be metered to said reducing catalyst. 27) The method ofclaim 26 wherein said step of determining said NSR includes the step ofusing said functional catalyst temperature to select a NSR valuerepresenting a desired stoichiometric based relationship between saidexternal reductant and said calculated NOx emissions. 28) The method ofclaim 12 further including the step of adjusting said NSR ratio by anadditional factor correlated to the ageing of said reducing catalystwhereby the rate of injection is reduced as said reducing catalyst ages.29) The method of claim 12 wherein said reducing catalyst is a zeoliteor a mixture of titanium, vanadium, tungsten, and/or molybdenum oxide.30) A method for determining the functional temperature of a catalyst inan exhaust system of a vehicle comprising the steps of i) determining,by sensing or calculating, the temperature of the exhaust, gases and thespace velocity of the exhaust gases through the catalyst; ii) filteringthe exhaust gas temperature by a catalyst filter to generate thefunctional temperature of the catalyst, the catalyst filter implementinga time constant determined as a function of changing space velocity tofilter the exhausts gas temperature. 31) The method of claim 30 whereinsaid exhaust gas temperature is the temperature of the exhaust gas,sensed or calculated, at the inlet of the reducing catalyst. 32) Themethod of claim 31 wherein said operating parameters sensed to determinethe temperature of said exhaust gas upstream of said SCR includes one ormore or the following: i) the engine coolant temperature with andwithout reference to the ambient temperature; ii) fueling and combustionair temperature; and, iii) the temperature of the exhaust gas upstreamof the SCR catalyst. 33) The method of claim 30 wherein said catalystfilter in the continuous time domain is represented by the transferfunction${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

where τ₁ equals τ₂ and is a function of the space velocity of theexhaust gases. 34) The method of claim 33 wherein said catalyst filteris in discreet form and implemented by a microprocessor, said filter insaid discrete form including two first order filters in series with oneanother. 35) The method of claim 34 wherein the first catalyst filter indiscrete form is represented by difference equation${{TCat}_{Filt1}(n)} = {\frac{{{TExhaust}(n)} - {{TCat}_{Filt1}\left( {n - 1} \right)}}{\tau_{Cat1}} + {{TCat}_{Filt1}\left( {n - 1} \right)}}$

and the second catalyst filter in discrete form is represented bydifference equation${{TCat}_{Filt2}(n)} = {\frac{{{TCat}_{Filt1}(n)} - {{TCat}_{Filt2}\left( {n - 1} \right)}}{\tau_{Cat2}} + {{TCat}_{Filt2}\left( {n - 1} \right)}}$

where τ_(CAT1) equals τ_(CAT2); TExhaust is said exhaust gastemperature; TCat_(Filt1) is the catalyst temperature after, firstfilter, intermediate temperature and TCat_(Filt2) is said functionalcatalyst temperature. 36) The method of claim 35 wherein$\tau_{CAT} = \frac{M_{CAT} \cdot {Cp}_{CAT}}{{SV} \cdot P_{GAS} \cdot {Cp}_{GAS} \cdot V_{CAT}}$

where M is the mass of the catalyst; V is the volume of the catalyst;Cp_(CAT) is the heat capacity of the catalyst; P_(GAS) is the density ofexhaust gas; Cp_(GAS) is the heat capacity of the exhaust gas; and, SVis the space velocity of exhaust gas. 37) The method of claim 30 furtherincluding the steps of sensing ambient temperature and upon shut down ofthe engine in said mobile application, filtering said functionalcatalyst temperature by the effect of said ambient temperature as afunction of the time said engine has been shut down or the differencebetween ambient and the cooled down temperature to determine afunctional cool down catalyst temperature and using said cool downtemperature as said functional catalyst temperature upon restart of saidengine. 38) The method of claim 37 wherein said step of filtering saidfunctional catalyst temperature to produce said cool down catalysttemperature is represented by a first order cool down filter, said cooldown filter implemented in the continuous time domain by the transferfunction ${H(s)} = \frac{1}{{\tau \cdot s} + 1}$

where τ is a function of time such as implemented by a timer or thedifference between catalyst temperature and ambient temperature atengine shut down. 39) The method of claim 30 further including the stepsof sensing ambient temperature after shut down of the engine andfiltering the catalyst temperature by a first order filter using a cooldown time constant established as a function of time elapsed from engineshut down at any given catalyst temperature at shut down or as afunction of the difference in temperature between ambient temperatureand catalyst shut down temperature whereby the catalyst temperature uponengine restart is determined. 40) A system for metering an externalreductant to a reducing catalyst in an SCR system applied to a vehiclepowered by an internal combustion engine comprising: a) means forsensing operating conditions of the vehicle and engine to generate, bycalculation and/or measurement, signals indicative of the actualquantity of NOx emissions emitted by the engine, the temperature of theexhaust gas and the space velocity of the exhaust gas; b) means forfiltering the actual NOx emission signal by an NOx time constant toproduce a calculated NOx signal different than the actual NOx signalwhen the NOx signal is changing and when the temperature of the catalystis within a set temperature range; c) means for filtering the exhaustgas temperature signal by a catalyst time constant to produce afunctional catalyst temperature signal different than the exhaust gastemperature when the space velocity signal changes; d) means forfactoring the functional catalyst temperature signal and the spacevelocity signal to generate a NSR signal indicative of a normalizedstoichiometric ratio of reductant to NOx emissions; and, e) means formetering the reductant to the reducing catalyst by factoring thecalculated NOx signal by the NSR signal to produce a metering signalcontrolling a metering device for the external reductant. 41) The systemof claim 40 wherein said means for filtering said NOx emissions includesan NOx filter and said means for filtering said exhaust gas temperatureincludes a catalyst filter; both said NOx and catalyst filters operablein a continuous time domain to perform a transfer function representedby the differential equation${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

where τ₁ equals τ₂ and is a function of the operation of said reducingcatalyst for said NOx filter and is a function of the space velocity ofthe exhaust gases for said catalyst filter. 42) The system of claim 41wherein both NOx and catalyst filters are implemented in discrete formas second order filters, each including a first order filter in serieswith a second first order filter. 43) The system of claim 42 wherein thefirst NOx filter in discrete form is represented by difference equation${{NOx}_{Filt1}(n)} = {\frac{{{NOx}_{EngOut}(n)} - {{NOx}_{Filt1}\left( {n - 1} \right)}}{\tau_{NOx1}} + {NOx}_{{Filt1}{({n - 1})}}}$

and the second NOx filter in discrete form is represented by differenceequation${{NOx}_{Filt2}(n)} = {\frac{{{NOx}_{Filt1}(n)} - {{NOx}_{Filt2}\left( {n - 1} \right)}}{\tau_{NOx2}} + {NOx}_{{Filt2}{({n - 1})}}}$

where τ_(NOx1) equals τ^(NOx2); NOx_(EngOut) is said actual NOxemissions; NOx_(Filt1) is the NOx value after said first filter and isan intermediate value, and NOx_(Filt2) is said calculated NOX emissions.44) The system of claim 43 wherein the first catalyst filter in discreteform is represented by difference equation${{TCat}_{Filt1}(n)} = {\frac{{{TExhaust}(n)} - {{TCat}_{Filt1}\left( {n - 1} \right)}}{\tau_{Cat1}} + {TCat}_{{Filt1}{({n - 1})}}}$

and the second catalyst filter in discrete form is represented bydifference equation${{TCat}_{Filt2}(n)} = {\frac{{{TCat}_{Filt1}(n)} - {{TCat}_{Filt2}\left( {n - 1} \right)}}{\tau_{Cat2}} + {TCat}_{{Filt2}{({n - 1})}}}$

where τ_(CAT1) equals τ_(CAT2); TExhaust is said exhaust gastemperature; TCat_(Filt1) is the catalyst temperature after firstfilter, intermediate temperature and TCat_(Filt2) is said functionalcatalyst temperature. 45) The system of claim 44 wherein said reducingcatalyst is a zeolite or a mixture of titanium, vanadium, tungsten,and/or molybdenum oxide. 46) A method for controlling dosage of anexternal reductant supplied to an SCR system including a reducingcatalyst in a mobile application having an IC engine to account fortransient NOx emissions produced by the engine, said method comprisingthe steps of: a) determining the actual NOx emissions produced by theengine to generate an NOx actual signal; b) filtering the NOx actualsignal when the reducing catalyst is within a set temperature change toproduce a variable delay in the NOx actual signal; and c) metering thereductant in real time at the value of the delayed NOx actual signal.47) The method of claim 46 where the filtering step is effected by anNOx filter having an NOx time constant determined as a function of thecapacity of the reducing catalyst at the temperature of the catalyst.48) The method of claim 47 wherein said time constant is a variablecorrelated to the time any given catalyst can store and/or release agiven quantity of reductant at a given catalyst temperature within saidset catalyst temperature range, said storage time decreasing as saidcatalyst temperature increases within said set temperature range. 49)The method of claim 47 wherein said NOx filter in a continuous timedomain filters the actual concentration of NOx emissions in accordancewith the transfer function${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

where τ₁ equals τ₂ and is a function of the operation of said reducingcatalyst. 50) The method of claim 49 wherein said NOx filter is indiscreet form and implemented by a microprocessor, said NOx filter insaid discrete form including two first order filters in series with oneanother. 51) The method of claim 50 wherein the first NOx filter indiscrete form is represented by difference equation${{NOx}_{Filt1}(n)} = {\frac{{{NOx}_{EngOut}(n)} - {{NOx}_{Filt1}\left( {n - 1} \right)}}{\tau_{NOx1}} + {{NOx}_{Filt1}\left( {n - 1} \right)}}$

and the second NOx filter in discrete form is represented by differenceequation${{NOx}_{Filt2}(n)} = {\frac{{{NOx}_{Filt1}(n)} - {{NOx}_{Filt2}\left( {n - 1} \right)}}{\tau_{NOx2}} + {{NOx}_{Filt2}\left( {n - 1} \right)}}$

where τ_(NOx1) equals τ_(NOx2); NOx_(EngOut) is said actual NOxemissions; NOx_(Filt1) is the NOx value after said first filter and isan intermediate value, and NOx_(Filt2) is said calculated NOx emissions.52) The method of claim 51 further including the step of determining thetemperature of said reducing catalyst by sensing or calculating thetemperature of the exhaust gas and filtering the temperature of theexhaust gas by a catalyst filter when the space velocity of the exhaustgas changes to establish a functional catalyst temperature. 53) Themethod of claim 52 wherein said catalyst filter in the continuous timedomain is represented by the transfer function${H(s)} = {\frac{1}{{\tau_{1} \cdot s} + 1} \cdot \frac{1}{{\tau_{2} \cdot s} + 1}}$

where τ₁ equals τ₂ and is a function of the space velocity of theexhaust gases. 54) The method of claim 53 wherein said catalyst filteris in discreet form and implemented by a microprocessor, said filter insaid discrete form including two first order filters in series with oneanother. 55) The method of claim 54 wherein the first catalyst filter indiscrete form is represented by difference equation${{TCat}_{Filt1}(n)} = {\frac{{{TExhaust}(n)} - {{TCat}_{Filt1}\left( {n - 1} \right)}}{\tau_{Cat1}} + {{TCat}_{Filt1}\left( {n - 1} \right)}}$

and the second catalyst filter in discrete form is represented bydifference equation${{TCat}_{Filt2}(n)} = {\frac{{{TCat}_{Filt1}(n)} - {{TCat}_{Filt2}\left( {n - 1} \right)}}{\tau_{Cat2}} + {{TCat}_{Fil2}\left( {n - 1} \right)}}$

where τ_(CAT1) equals τ_(CAT2); TExhaust is said exhaust gastemperature; TCat_(Filt1) is the catalyst temperature after firstfilter, intermediate temperature and TCat_(Filt2) is said functionalcatalyst temperature. 56) The method of claim 55 wherein$\tau_{CAT} = \frac{M_{CAT} \cdot {Cp}_{CAT}}{{SV} \cdot P_{GAS} \cdot {Cp}_{GAS} \cdot V_{CAT}}$

where M is the mass of the catalyst; V is the volume of the catalyst;CP_(CAT) is the heat capacity of the catalyst; P_(GAS) is the density ofexhaust gas; Cp_(GAS) is the heat capacity of the exhaust gas; and, SVis the space velocity of exhaust gas. 57) The method of claim 46 furtherincluding the steps of sensing ambient temperature after shut down ofthe engine and filtering the catalyst temperature by a first orderfilter using a cool down time constant established as a function of timeelapsed from engine shut down at any given catalyst temperature at shutdown or as a function of the difference in temperature between ambienttemperature and catalyst shut down temperature whereby the catalysttemperature upon engine restart is determined.